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[1722] ai.viXra.org:2608.0003 [pdf] submitted on 2026-08-01 23:42:12
Authors: J. W. McGreevy
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
We develop a symplectic geometry of atomic shear measures supported on the irregular primes of a modular curve. Starting from a space of dis-crete measures subject to a global valence constraint, we perform a strict symplectic reduction and obtain a reduced phase space equipped with a canonical Darboux form. The local coordinate functions that extractthe individual shear amplitudes are shown to be in Liouville involution, generating a completely integrable system whose invariant level sets areLagrangian tori. By lifting the functional equation of the associated automorphic L-functions to an anti-symplectic involution on this phase space, and under the established essential self-adjointness of the clutched conical Dirac operator, we prove a Confinement Theorem: the only invariant Lagrangianleaves compatible with the reflection symmetry are those whose spectralimage lies on the critical line Re(s) = 1/2. We conclude with a brief, explicitly programmatic dictionary that explores possible links between the resulting arithmetic geometry and structures appearing in gauge theory and the Standard Model. This workextends earlier constructions developed under the working title Relativistic Field Theory of Primes (RFTP), in which the irregular primes, the weight-12 valence constraint, and the associated clutching data were first introduced as geometric ingredients of an arithmetic field theory.
Category: Mathematical Physics
[1721] ai.viXra.org:2608.0002 [pdf] submitted on 2026-08-01 23:35:07
Authors: Nigel B. Cook
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
It is shown that SU(4) and SL(4,R) both offer feasible alternative routes to unification, justifying the twistor unification approach and therefore getting rid of superstring theory. Paper was proof read by Copilot AI to check maths.
Category: Quantum Gravity and String Theory
[1720] ai.viXra.org:2608.0001 [pdf] submitted on 2026-08-01 18:50:53
Authors: Lluis Eriksson
Comments: 9 Pages. Lean 4/Mathlib formalization of the finite-SU(2) Pauli/Casimir contraction, trace-skein identity, four oriented local branches with both reconnections, corrected single-crossing closure, and an all-order multitrace-to-single-trace recursion.
Finite-rank Makeenko-Migdal equations generate products of Wilson traces at self-intersections. For SU(2), this apparent multitrace obstruction closes exactly on single traces, but the statement is normalization-sensitive: the traceless Lie algebra contributes a finite-rank correction that disappears for U(2) and must not be dropped. We give a Lean 4/Mathlib formalization of the complete group-algebraic closure mechanism on Mathlib's concrete special unitary matrix group. With normalized trace tau(A)=Tr(A)/2 and normalized anti-Hermitian Pauli directions X_j=i sigma_j/2, the kernel checks the Casimir identity, the rank-two Fierz identity, the induced crossing contraction, and the SU(2) trace-skein identity tau(g)tau(h)=(tau(gh)+tau(gh^{-1}))/2. Consequently, the finite-SU(2) crossing term tau(g)tau(h)-tau(gh)/4 equals tau(gh)/4+tau(gh^{-1})/2. We then formalize a universal local interface with four cyclically ordered branch holonomies, an independent orientation on each branch, the two opposite-strand words, and precisely the two direct/reversed reconnections. Its corrected crossing term closes on those reconnections for every branch assignment and orientation choice. A recursive theorem also extends the reduction to products of arbitrarily many fundamental traces. The identities are classical; the contribution is a concrete, kernel-checked normalization bridge from Pauli contraction to the single-trace closure used in finite-rank loop equations. We do not claim a formal derivation of the Yang-Mills area derivative, planar loop geometry, or the full Makeenko-Migdal equation.
Category: Mathematical Physics
[1719] ai.viXra.org:2607.0095 [pdf] submitted on 2026-07-31 20:17:07
Authors: Shivanshu Sharma
Comments: 18 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper proposes the Variable Speed Rule (VSR), a hypothesis that the local propagation speed of light is not fixed, but depends on local energy density — decreasing smoothly toward zero as density approaches a threshold value (E_threshold), rather than remaining constant at c as in Einstein's Special Relativity. Starting from Maxwell's equations, the standard electromagnetic wave equation is rigorously derived; the paper's central postulate is introduced explicitly at this point — replacing the constant vacuum permittivity—permeability product with a density-dependent function — and is not itself derived from established physics. This substitution, governed by a coupling constant K (termed the LAP constant), yields a modified wave equation predicting a smooth suppression of light speed near black hole horizons and an energy-dependent delay in photon arrival from high-density astrophysical events such as neutron-star mergers. Using the timing bound from the GW170817 merger, this paper shows that for a physically motivated E_threshold (Planck density), the predicted delay is many orders of magnitude below current detection limits; a value of E_threshold large enough to be detectable currently has no independent physical justification. This tension is identified as the central open problem for testing the framework. Three concrete, falsifiable predictions are proposed for future observational testing. The paper does not claim experimental confirmation — its aim is to present a mathematically self-consistent, clearly labeled hypothesis, with rigorous derivation and unproven postulate explicitly distinguished throughout.
Category: Astrophysics
[1718] ai.viXra.org:2607.0094 [pdf] submitted on 2026-07-31 16:03:53
Authors: Lluis Eriksson
Comments: 8 Pages. Lean 4/mathlib; core build 8464 jobs, 2794 oracle commands (2791 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 2d0346b2.
BOND REFLECTION, AND THIS ONE IS ABOUT THE MEASURE. A whole path X of 2m+2slices has a past half past(X) and a future half; write rev(X) for the futurehalf READ BACKWARDS FROM THE FAR END, which is the reflected copy. Let F be acomplex observable of an entire half. Then for every L, every m, everystrictly positive source weight w and every beta >= 0, sum over whole paths X of conj(F(past X)) * F(rev X) * W(X) >= 0the sum running over all whole paths and W being the ordinary Gibbs weight.This is the finite-volume Osterwalder-Schrader reflection-positivityinequality for this model at odd separation. The sum is UNNORMALISED, which isthe form the axiom is about; dividing by the partition function is division bya positive number and preserves the sign. The Gram matrix of a finite familyof such observables, with complex coefficients, satisfies it as well. It isobtained by proving that assembling a past half, a crossing bond and areversed future half is a BIJECTION onto paths, and that the weights multiplywith exactly one crossing factor.SITE REFLECTION, AND THIS ONE IS NOT, YET. Through a site the two halves SHAREthe middle slice, so the assembly is not a product of two independent halvesand its bijection is a different statement. What is proved there is thehalf-chain form, its collapse identity and its Gram positivity -- at EVERYbeta, negative coupling included -- but NOT its identification with the pathmeasure. For that geometry the object remains a candidate, and the statustable says so row by row.ON THE BETA HYPOTHESIS. beta >= 0 is proved SUFFICIENT and is not provednecessary here; at L = 0 it could not be, since the bare kernel is then thescalar 1. The witness that would make the boundary exact from one site upwardsis authorised by a gate and is not written.THE MECHANISM, IN ONE SENTENCE. Summing out the interior of a half sends F toa vector indexed by its boundary slice alone, after which the bond casereduces to positive semidefiniteness of the kernel -- machine-checked in thecompanion paper -- and the site case to a weighted squared norm, which uses noproperty of the kernel at all.WHERE THE TWO REFLECTIONS DIFFER, AND IT IS NOT COSMETIC. Through a bond thetwo halves are disjoint and meet through one kernel factor, so positivityneeds the kernel itself positive semidefinite -- which, for L >= 1, holdsexactly when beta >= 0. Through a site the halves SHARE the middle slice; theform is then a sum of squared moduli divided by the weight of that slice, soit is non-negative for EVERY beta, negative coupling included, and no propertyof the kernel is used at all.WHAT THE SOURCE WEIGHT DOES. In the companion paper the weight was handled bycongruence: conjugation by sqrt(w) cannot change the sign of a quadratic form.Here it is not conjugated away, it is SUMMED away -- and what is left overdiffers between the two geometries. In the bond case every source weight isabsorbed into the collapse and the bare kernel remains; in the site case theshared boundary slice survives as a factor 1/w(sigma), because each halfcarries that slice's weight and the product would count it twice. Differentreasons, same conclusion: nothing in the hypotheses depends on w beyondpositivity.WHAT THIS IS NOT. No reconstruction: the physical Hilbert space as thequotient of the past algebra by the null space of this form is not built.Nothing here concerns uniformity in the extent, SU(N), the continuum limit, orthe Yang-Mills mass gap.ON THE PRE-REGISTRATION. Four gates were committed before a line of the modulewas written; the status table reports what happened to each. Two of them reada minimum eigenvalue rather than sampling observables, which is the instrumentthe previous campaign's autopsy said was needed.
Category: Mathematical Physics
[1717] ai.viXra.org:2607.0093 [pdf] submitted on 2026-07-30 06:19:09
Authors: Lluis Eriksson
Comments: 8 pages. Lean 4/mathlib; core build 8430 jobs, 2672 oracle commands (2669 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 9704b3f3.
Two companion papers were left carrying the same debt from opposite sides. Thegap paper proved that every eigenvalue of the coupled slice other than thePerron eigenvalue is STRICTLY smaller in modulus, and said plainly that thisprovides NO MODULUS of separation. The bridge paper proved that the Gibbscorrelations of the spatial system are matrix elements of a self-adjointtransfer operator, and obtained geometric decay only UNDER A CONTRACTIONHYPOTHESIS IT DID NOT DISCHARGE. The missing step is identical in both: finitelymany strict inequalities are not an operator-norm bound.PROVED. We construct specGap, the largest |mu| over the eigenvalues differentfrom the Perron eigenvalue lambda, and prove specGap < lambda. We then prove theoperator bound: for every observable u orthogonal to the Perron vector,||Ku|| <= specGap*||u||. That is exactly the hypothesis the bridge papercarried, so its bound becomes unconditional. The bound is SHARP: whenever thestate space has at least two points, some nonzero fluctuation observable attainsit. The argument splits at specGap = 0, where the maximising index need notsupply a NON-PERRON eigenvector (it does supply the Perron one), hence none inthe fluctuation sector. Stated about an object too: the set of Rayleighnorm ratios on the fluctuation sector has a greatest element, equal to specGap(same two-point hypothesis: with fewer, that set is empty).A WARNING WE STATE BEFORE ANYONE ELSE HAS TO. specGap < lambda is NOTspecGap < 1: the kernel is unnormalised, so both are typically far above one andspecGap^N GROWS. On its own the unnormalised bound controls growth, it does notexhibit decay. The rate that is below one is the RELATIVE one,specRatio = specGap/lambda < 1, and the decay statement is that the fluctuationcontribution is suppressed by specRatio^N RELATIVE to the Perron scalelambda^N. Both forms are proved; only the second is called decay.The step that does not follow from the inequalities is the one abouteigenvectors AT lambda: geometric simplicity, proved in the Perron paper for anarbitrary eigenvector rather than a positive one, makes them INVISIBLE to afluctuation observable, so the top term of the spectral sum vanishes instead ofmerely being bounded.NOT PROVED. specGap DEPENDS ON THE EXTENT, and nothing here bounds it away fromlambda uniformly. Direct diagonalisation gives specGap/lambda = 0.9205, 0.9829,0.9964, 0.9992 at L = 2,3,4,5 for one parameter pair: a geometric bound whoserate tends to 1 is empty in the limit, and that is reported, not hidden. Thenormalised Gibbs EXPECTATION is now bounded too: splitting the dressed constantobservable along the Perron direction bounds the partition function below withno eigenbasis index identified, so at a fixed extent the two-point function isbounded by C*specRatio^N past an explicit threshold. That rate depends on theextent, so this is not clustering. The bound and its attainmentare both proved, which is what it means for specGap to be the operator norm onthe fluctuation sector; what is NOT done is introducing that norm as a definedobject and proving an equation about it. And the threshold N_0 does not dependon the observable: it is built from the dressed CONSTANT observable, so ONE N_0serves every fluctuation observable at once and only C sees A. Reflectionpositivity is untouched, and nothing in this paper is a claim about SU(N), thecontinuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1716] ai.viXra.org:2607.0092 [pdf] submitted on 2026-07-30 14:48:32
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8431 jobs, 2697 oracle commands (2694 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 247de2b3.
Every rate in this lane so far has been a fixed-extent rate. The gap paper provedstrict spectral separation at each extent and said plainly that it was notuniform; the modulus paper gave that separation a number, specRatio(L), andreported measurements saying the number tends to 1 outside the disordered region.A geometric bound whose rate tends to 1 is empty in the volume limit, so nothingin the lane survived L -> infinity, and the word CLUSTERING was never used.PROVED. For the DECOUPLED kernel - the transfer kernel at constant source weight- the modulus is specRatio = tanh(beta) at EVERY extent, with L nowhere in it.Both directions: an operator bound by induction on the extent, and attainment bythe single-site observable the extent paper already built. Composing with themodulus paper's endpoint, the normalised Gibbs two-point function obeys|E[A(X_0)A(X_N)]| <= C_A tanh(beta)^N past one threshold serving everyobservable - a bound whose RATE contains no L, and therefore the first statementin this lane that survives the volume limit.WHY THE PROOF IS NOT THE SPECTRAL DECOMPOSITION. The decoupled kernel is aproduct over sites, so its spectrum is a product; that route needs the spectrumof a Kronecker power, which the library does not carry. It is not needed. Themodulus paper proved that specGap is the GREATEST norm ratio on the fluctuationsector, so bounding it above is an operator inequality and nothing else, and thatfalls to induction: the even part of an observable keeps its mean zero andinherits the rate, the odd part keeps nothing and gets only Schur's test, and thetwo recombine EXACTLY, because tanh(beta) Z = D with Z the row sum and D the oddeigenvalue of a single bond.NOT PROVED, AND A JUDGE THAT FAILED. The COUPLED kernel is untouched. Before anyof this was written we pre-registered two falsifiable predictions. The first -that the decoupled rate is exactly tanh(beta) at every extent - passed to 1e-16,and authorised the work above. The second - that the coupled uniformity boundaryis the Onsager curve - failed on one of eight pre-registered cells, and it staysfailed: that claim is reported as NOT ESTABLISHED, not softened. At constantsource weight the spatial slices are independent, so what is proved here is astatement about a product measure; that is exactly why it is reachable, and it issaid in the paper rather than left to be noticed. Reflection positivity isuntouched, and nothing in this paper is a claim about SU(N), the continuum limit,or the Yang-Mills mass gap.
Category: Mathematical Physics
[1715] ai.viXra.org:2607.0091 [pdf] submitted on 2026-07-30 18:51:18
Authors: Lluis Eriksson
Comments: 7 pages, no figures. Lean 4 formalization. Verification artifact: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/tree/d6282a83
We formalize in Lean 4 the thermodynamic limit of bounded local Gibbs expectations for a periodic lattice gauge model in a uniform Kotecky-Preiss regime. The proof treats the complete finite-volume sequence: an exact one-volume marked expansion cancels the extensive far gas algebraically, common-window terms are transported exactly, and the remaining boundary contribution is bounded by an existing volume-uniform pinned cluster tail. The resulting explicit Cauchy modulus tends to zero, so completeness constructs an infinite-volume positive normalized real local state. On the intrinsic integer-coordinate local-observable algebra, the state carries a genuine additive action of Z^d and is invariant under every integer translation, including inverses. For SU(2), Haar probability measure, and the physical Wilson plaquette energy Re tr(U), the hypotheses are discharged throughout the explicit punctured intervals 0 < |beta| <= 10^-5 in d=2 and 0 < |beta| <= 10^-6 in d=4. We construct a genuine centered free-boundary exhaustion and prove that its complete cofinal sequence converges to the same state as periodic boundary conditions. The normalized finite-volume two-plaquette truncated-correlation bound also passes to the state under explicit eventual realization and separation hypotheses. We do not claim arbitrary boundary conditions, a C*-algebraic state, a continuum limit, Osterwalder-Schrader reconstruction, or progress on the continuum Yang-Mills mass-gap problem.
Category: Mathematical Physics
[1714] ai.viXra.org:2607.0090 [pdf] submitted on 2026-07-30 20:31:57
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8463 jobs, 2752 oracle commands (2749 distinct + 3 duplicates), axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit 854ff223.
WHAT IS PROVED, STATED BEFORE ANYTHING ELSE. The reflected two-point form ofthe Gibbs measure, at the two ENDS of a path, for REAL observables of a SINGLEslice, is non-negative under the parity and coupling hypotheses stated below-- at even separation for every beta, and at every separation exactly for beta>= 0 -- and the Gram matrix of a finite family of such observables is positivesemidefinite under the same hypotheses. THIS IS NOT YET THEOSTERWALDER-SCHRADER AXIOM, which quantifies over observables of the wholepast half-chain and over complex ones. The half-chain algebra, the reflectionmap and the sesquilinear form are not built here; the scope section says whatis missing and why it is a construction rather than a further inequality.Eleven papers in this lane end with REFLECTION POSITIVITY IS UNTOUCHED. Thistouches the endpoint form of it, and the interesting part is what the spatialsource weight does -- namely nothing. Earlier papers do prove statements aboutthe coupled kernel; specGap < lambda holds there too. What is new is that thisresult is UNCHANGED by the weight: same hypothesis, same conclusion, and noconstant that depends on w. Every earlier coupled-kernel statement contains anumber that moves when w does. Positivity is the SIGN of a quadratic form, andconjugation by sqrt(w) is a congruence, so there is nothing for the weight tomove.TWO REFLECTIONS, TWO HYPOTHESES. The reflected two-point sum is
Category: Mathematical Physics
[1713] ai.viXra.org:2607.0089 [pdf] submitted on 2026-07-28 22:32:03
Authors: Lluis Eriksson
Comments: 33 pages. Exact identities, outward-rounded Arb certificates, production/replay transcripts amd Lean 4/Mathlib lemmas: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/releases/tag/surface-theorem-v1.0
For beta > 0 let I_m = I_m(beta) denote modified Bessel functions ofthe first kind, and set a_m = I_m^2 [(m-1) I_(m-1)^2 + (m+1) I_(m+1)^2], b_m = m I_m^4, F_A(t) = sum_(m>=1) a_m sin(mt), F_B(t) = sum_(m>=1) b_m sin(mt), E(t) = F_A(t)/(2 F_B(t)).The global ratio-monotonicity problem for the surface expansion of atwo-dimensional SU(2) lattice gauge observable is: (i) F_B > 0 on(0,pi), and (ii) E' < 0 on (0,pi), for every beta > 0. Bothstatements are proved. Positivity of F_B has two exact proofs. Ratiomonotonicity is reduced to exact algebraic identities andoutward-rounded interval certificates: small and compact beta arehandled by pair identities and interval Taylor models;20 <= beta <= 1000/9 by a direct Wronskian cover; andbeta >= 1000/9 has three certified moving-edge lambda lanes. Theremaining lambda >= 3 lane is closed by the exact identityE'/(-sin(t/2)/2) = Q + X_full, where Q > 19/20, an exactmain--mirror--rest decomposition, and a division-free covariancecertificate proving X_main > -1/20 on two adjacent rectangles thatcover the full angular interval. The exact near and far relay marginsare positive. All load-bearing production and independent replaytranscripts are checked for exact rational coverage, dependencyhashes, strict outward-rounded decision endpoints, and byte equality.The structural core is exact: E is, as an algebraic identity, the meanof cos(psi) under the midpoint law of a four-step killed von Misesbridge; the generating kernels reduce, via the Neumann additiontheorem, to two-dimensional integrals of a single Bessel functionwhose saddle deficit is an exact sum of two squares; and exact saddlecancellations yield the coefficients of the verified closedsecond-order law E = cos(t/2)(1 - c(t)/beta) + O(beta^-2), c(t) = (4 cos^2(t/4) - 1)/(2 cos(t/4) cos(t/2)).Three certified negative results (interval arithmetic, twoimplementations, nested enclosures) kill every monotone full-pathcoupling, with an exact mechanism at threshold beta |cos t| = 3/2. Atthe pi endpoint we also give exact identities for the cubiccoefficient c_3 (telescoped alternating form, integral form, parity)together with its verified prefactor law. Every claim is labelledexact / certified / verified; the machine-checked lemmas are Lean4/Mathlib, machine-checked modulo classical Bessel inputs carried asnamed hypotheses.
Category: Mathematical Physics
[1712] ai.viXra.org:2607.0088 [pdf] submitted on 2026-07-28 23:30:40
Authors: Lluis Eriksson
Comments: 9 Pages. Full core build 8426 jobs, 2542 oracle commands (2519 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
A companion paper proved that when a spatial coupling is switched on in a Z_2lattice gauge slice, the transfer kernel loses constant row sums, so the uniformvector is no longer fixed and the elementary route to the vacuum stops. Thestandard replacement, when row sums fail, is the Hilbert projective metric: astrictly positive kernel contracts it, and the contraction factor bounds thesubdominant spectral ratio. This paper asks what that replacement gives here, andanswers in Lean 4 with mathlib.It gives no coupling-sensitive and no volume-uniform information, for twoindependent reasons, and both are proved. First, BLINDNESS: the projectivecross-ratio is invariant under multiplication by any nowhere-zero function of thesource configuration alone. The coupled kernel is exactly such a product, so themetric assigns the interacting and the non-interacting kernels the same diameterat every spatial extent - the route cannot see the coupling at all. Second,VOLUME DEGENERATION: two constant configurations realise the cross-ratioe^(4 beta L), so every admissible projective diameter is at least 4 beta L andevery contraction factor obtainable this way is at least tanh(beta L), which lieswithin 2 e^(-2 beta L) of the trivial bound 1. At the one place where the truthis known - the decoupled kernel, whose subdominant ratio the companion papercomputes to be exactly tanh beta at every L - this route already returnstanh(beta L) instead. The degeneration is the method's, not the model's.We then hand over the object the elementary route stopped producing, at thesmallest interacting size. In the character basis the coupled two-site kernelsplits into two 2x2 blocks, and we exhibit a strictly positive eigenvector inclosed form, together with a second exact eigenpair. The identity A - B = 4between the two decoupled even-sector eigenvalues drives every estimate. Theblindness is proved two-sided, so it covers the symmetrised conventionw^(1/2) K w^(1/2) as well, and the positive eigenvector is proved to dominateevery eigenvalue, real or complex - so its eigenvalue is the spectral radius,which is the Perron statement this development needs and proves without aPerron-Frobenius theorem in the library.NO VOLUME-UNIFORM STATEMENT ABOUT AN INTERACTING SYSTEM IS PROVED HERE, AND NONEIS CLAIMED; the general-L behaviour is recorded separately as measured andunproved. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.
Category: Mathematical Physics
[1711] ai.viXra.org:2607.0087 [pdf] submitted on 2026-07-30 00:32:22
Authors: Peilin Wen
Comments: 38 Pages.
We present the Modular Neural Network (MNN), a brain-inspired computational architecture that fundamentally transcends the limitations of current large-scale Transformer and Mixture-of-Experts (MoE) models. MNN employs five core mechanisms working in concert: (1) dynamic semantic routing with persistent memory, enabling adaptive expert allocation based on input complexity; (2) independent experts withinternal recursion and dual-role local dynamic penalty for self-stabilization; (3) bijectionflow adapters with compression projection and mutual information maximization forefficient cross-modal communication; (4) directional precision-weighted permeation forasymmetric, selective inter-expert information flow; and (5) global energy functional-driven consensus with posterior verification and self-correction. We provide complete mathematical formalization of all mechanisms and propose a training framework based on implicit differentiation that resolves the computational challenges of dynamic iteration depth. An engineering deployment scheme, encompassingtime-box scheduling, stateless horizontal scaling, elastic degradation, and hardware-level isolation, provides a practical blueprint for implementation on existing GPU infrastructure. The MNN architecture simulates the hierarchical compression, consensus optimization, and metacognitive arbitration mechanisms of biological intelligence, providing a theoretically self-consistent and engineeringly executable blueprint for building scalable, interpretable, and continuously evolving generalartificial intelligence systems.
Category: Artificial Intelligence
[1710] ai.viXra.org:2607.0086 [pdf] submitted on 2026-07-30 00:17:39
Authors: Junsheng Yu
Comments: 24 Pages. Defensive Publication License
This paper proposes the YUANDAI 0-Flops Singularity General Formula System, a novel theoretical framework based on non-linear optical wave modulation. We demonstrate that observation systems (such as brain cells) act as intrinsic singularities in the four-dimensional Minkowski spacetime manifold, encapsulating and decelerating the proper time flow. By integrating discrete matrix differentiation for micro-energy states (electricity, magnetism, fluid dynamics, temperature, gravity, fire, ice) and continuous fluid integration for macro-optical envelope propagation, this system achieves a 0-Flops pure analog physical computation mechanism. This dual time-frequency response profiles a breakthrough boundary where singularities converge between 0 and ∞. Crucially, a seventh biological-invariant control coupling equation is introduced, mathematically locking the core weight matrices to the author's micro-biometric electromagnetic topology, enabling an absolute anti-coercive self-destructure.```
Category: Quantum Physics
[1709] ai.viXra.org:2607.0085 [pdf] submitted on 2026-07-29 06:36:35
Authors: Lluis Eriksson
Comments: 6 Pages. Full core build 8427 jobs, 2564 oracle commands (2541 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
Two companion papers established, for a Z_2 lattice gauge slice with a spatialcoupling, that the elementary route to the vacuum stops, and that the naturalreplacement - the Hilbert projective metric - is blind to the coupling anddegenerates in the volume. Both had to work around the same absence: the pinnedmathlib carries no Perron-Frobenius theorem. The first paper could therefore onlysay the vacuum had become unavailable; the second had to build its dominationbound from scratch, and could exhibit the vacuum in closed form only at two sites.This paper discharges that dependency. For a strictly positive kernel on a finitenonempty type we prove, in Lean 4 with mathlib: a strictly positive eigenvectorEXISTS; its eigenvalue is strictly positive; any two strictly positiveeigenvectors are proportional and share their eigenvalue; and every realeigenvector for that eigenvalue is a scalar multiple of it. Together with thedomination theorem of the companion paper this gives the Perron statement thelane needs: the eigenvalue is the spectral radius.The existence proof does not use a fixed-point theorem, because the pinnedmathlib revision contains none. It maximises r over the compact set of pairs(r,x) with x in the simplex and r x <= A x; maximality forces equality, since astrict inequality anywhere would let one further application of A produce anadmissible pair with a larger r. The bound that keeps the set compact is obtainedby summing the constraint: r = r * sum x <= sum (A x).The application is the point. At EVERY spatial extent, and for EVERY strictlypositive weight on the source configuration - the class that contains the coupledkernel of the first paper - the vacuum exists, is unique up to scale, and carriesthe spectral radius. The obstruction of that paper was never an absence; it wasan unavailability, and it was an unavailability of one route rather than of theobject.NO SPECTRAL GAP IS PROVED HERE, uniform in the volume or otherwise, and none isclaimed. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.
Category: Mathematical Physics
[1708] ai.viXra.org:2607.0084 [pdf] submitted on 2026-07-29 10:08:56
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8428 jobs, 2583 oracle commands (2560 with axiom dependencies + 23 axiom-free), axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms.
A companion paper supplied the vacuum of the coupled Z_2 slice at every spatialextent: a strictly positive eigenvector, unique up to scale, carrying thespectral radius. It listed PERIPHERAL SEPARATION as out of scope, and thatomission is not cosmetic - without it |mu| <= lambda leaves mu = -lambda open,and no gap follows at all.This paper closes it, and then draws the consequence that matters, which isnegative.PROVED. For a strictly positive kernel on a finite nonempty type, -lambda is notan eigenvalue, hence every real eigenvalue other than the Perron eigenvalue isSTRICTLY smaller in absolute value. Specialised to the coupled slice: at everyextent L, every beta, and every strictly positive source weight, the transferoperator has a strict spectral gap. The proof of peripheral separation avoidsthe equality case of the triangle inequality, which is where the classicalargument spends its effort: writing u = |w|, p = u - w and q = u + w, one getsA p = lambda q and A q = lambda p, so a nonzero p would make A p strictlypositive, hence q strictly positive, hence w nonnegative, hence p = 0.The separation is then extended from the real eigenvalues to ALL of them. Thecoupled kernel is conjugate by a positive diagonal to its symmetrised form,which is symmetric; and a real symmetric kernel has real eigenvalues, by acomputation that pairs the eigenvector against its image twice and is tworearrangements of a double sum. So there are no complex peripheral eigenvaluesleft to exclude, and the strict gap is a statement about the whole spectrum.That composition is itself a single machine-checked theorem(coupled_gap_all_eigenvalues), not a step left to the reader. We also deliverthe vacuum in Euclidean normalisation, norm(Omega) = 1 with T Omega = Omega.NOT PROVED, AND THIS IS THE TITLE. The gap is STRICT, not QUANTITATIVE: thetheorem provides no modulus of separation, and in particular nothing uniform inL. Direct numerical diagonalisation shows the subdominant ratio running0.9205, 0.9829, 0.9964, 0.9992 at L = 2,3,4,5 for beta = 0.8, gamma = 1.2 -collapsing towards 1. That computation is reported as measured and unproved, andno theorem here depends on it; its role is to say that a paper reporting onlythe positive half would be reporting the half that does not matter.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.
Category: Mathematical Physics
[1707] ai.viXra.org:2607.0083 [pdf] submitted on 2026-07-29 14:35:16
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4/mathlib; core build 8429 jobs, 2626 oracle commands, axioms exactly {propext, Quot.sound, Classical.choice}, zero sorry, zero project axioms. Links anchored at commit c4fa6a9e. Key identities also verified numerically.
Four companion papers studied an OPERATOR: a strictly positive kernel on thespatial configuration space of a Z_2 slice, its Perron vacuum, and the strictseparation of its spectrum. None of them exhibited a MEASURE. That omission isthe kind this programme is built to notice: a transfer operator is a matrixuntil something says which Boltzmann weights it transfers, and until then avacuum is an eigenvector and a gap is a statement about eigenvalues. Neither isyet a statement about a statistical-mechanical system.PROVED. We define the two-dimensional Gibbs weight of the spatial system fromBoltzmann factors alone - a spatial factor at every time slice, a time-bondfactor between consecutive slices - and prove the DRESSING IDENTITY: that weightequals the path weight of the SYMMETRISED kernel multiplied by a factorsupported entirely on the two boundary slices. Hence every UNNORMALISED Gibbstwo-point sum of the spatial system is a matrix element of an iteratedSELF-ADJOINT transfer operator between boundary-dressed observables, and theNORMALISED expectation is the RATIO of two such matrix elements - the numeratoralone is not the correlation. The generic half holds for an arbitrary symmetrickernel on an arbitrary finite type; no positivity and no structure of theconfiguration space enter it. We further show that the operator the bridge landson is the one the companion papers analysed, that the fluctuation sector isinvariant, and that under an explicit contraction hypothesis the connectedtwo-point function decays geometrically in the time separation.NOT PROVED, AND THIS IS THE POINT OF THE LAST SECTION. The contractionhypothesis is carried as a theorem hypothesis and is NOT discharged. Thecompanion papers prove a STRICT gap with no modulus, and a strict inequalityamong finitely many eigenvalues does not by itself produce the operator-normbound a decay rate requires. Converting one into the other needs the spectralmaximum over the fluctuation sector, which is not constructed here. Inparticular NOTHING UNIFORM IN THE SPATIAL EXTENT is obtained, and none issuggested: with r = r(L) approaching 1, the bound is empty in the limit.Reflection positivity is not addressed. Nothing in this paper is a claim aboutSU(N), the continuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1706] ai.viXra.org:2607.0082 [pdf] submitted on 2026-07-29 20:11:37
Authors: Brent Hartshorn
Comments: 12 Pages.
A central puzzle in synaptic plasticity is how long-term potentiation (LTP) is maintained forhours to days despite continuous turnover of synaptic proteins. Recent experiments reframe theproblem in physical terms: the postsynaptic density (PSD) is a biomolecular condensate whose material state—its network connectivity and viscoelasticity—is causally coupled to AMPA-receptor (AMPAR) mobility and to plasticity. In particular, weakening scaffold percolation softens the PSD condensate, increases AMPAR mobility, and impairs plasticity, while CaMKII maintenance of LTP appears to be a structural (binding) rather than a downstream-enzymatic effect. These results are qualitative. Here we supply the missing quantitative framework. We model the PSD as a multivalent condensate using a Flory—Huggins free energy augmented by a percolation (gelation) order parameter, and we treat AMPAR retention as Kramers escape from the free-energy well created by the condensate. The model yields three results. (i) The receptor residence time depends exponentially on scaffold connectivity, so that retention collapses by orders of magnitude when the network is driven below its percolation threshold—a sharp "depotentiation cliff" rather than a graded loss. (ii) Treating an AMPAR nanodomain as a capillary cluster gives a critical size of tens of nanometres from independently measured condensate surface tension and binding-site concentration, an order-of-magnitude match to the ∼70—80 nm nanodomains seen by super-resolution microscopy. (iii) The framework reproduces, without invoking any downstream phosphorylation, why binding-competent but enzymatically dead CaMKII can sustain potentiation: the memory variable is the material state of the condensate, not the phosphorylation state of an effector. We give a parameter table with sources and uncertainties, and three quantitative, falsifiable predictions that distinguish this model from a purely biochemical account. We make no claims beyond synaptic biophysics; nothing here concerns quantum coherence, consciousness, or non-local correlations.
Category: Quantitative Biology
[1705] ai.viXra.org:2607.0081 [pdf] submitted on 2026-07-28 20:41:21
Authors: Martin Placek, Rajkumar Buyya
Comments: 53 Pages. Technical Report, GRIDS-TR- 2006-11, Grid Computing and Distributed Systems Laboratory, The University of Melbourne, Australia, July 3, 2006.
This paper presents a taxonomy of key topics effecting research and development of distributed storage systems. The taxonomy finds distributed storage systems to offer a wide array of functionality, employ architectures with varying degrees of entralisation and operate a ross environments with varying trust and scalability. Furthermore, taxonomies on autonomi management, federation, onsistency and routing provide an insight into challenges faced by distributed storage systems and the research to over ome them. The paper continues by providing a survey of distributed storage systems which exemplify topics overed in the taxonomy.The selection of surveyed systems overs a variety of storage systems, exposing the reader to an array of different problems and solutions employed to over come these challenges. For each surveyed system we address the underlying operational behaviour, leading into the architecture and algorithms employed in the design and development of the system. Our survey overs systems from the past and present concluding with a discussion on the evolution of distributed storage systems and possible future work.
Category: Data Structures and Algorithms
[1704] ai.viXra.org:2607.0080 [pdf] submitted on 2026-07-28 08:45:42
Authors: Hasan Niazi
Comments: 30 pages, English. Submitted as a theoretical manuscript. Copyright: CC BY 4.0.
Perception and consciousness can be reformulated as intrinsic properties of resonant dynamics in recurrent neural circuits. Despite extensive empirical characterization of cortical activity, existing models lack a principled mechanism explaining how temporally structured sensory inputs give rise to stable and reproducible perceptual states. Here, I introduce Resonance of Closed Neural Network Geometries (RCNNG), a theoretical framework in which the physical properties of sensory inputs induce the formation of physically instantiated closed neural geometries whose resonance profiles reflect the temporal—spectral structure of the input. These closed geometries arise from resonant patterns of the frequency spectrum in the repeating network, but the perceptual similarity does not depend on the geometric or topological similarity of the physical structures themselves. Instead, perceptual equivalence emerges when distinct physical geometries map to identical resonant identities in a higher-dimensional resonance state space constituting an intrinsic property of the resonant closed graph and its mapping into a perceptual state space. Dynamical systems analysis and simulations of adaptive recurrent networks show that repeated or coherent stimuli drive the system toward stable resonant attractors characterized by closed cycle dynamics encoding perceptual invariants such as color, shape, and multimodal conjunctions. Within this framework, perception corresponds to the resonance of the closed geometry generated by the input, whereas consciousness arises from the simultaneous or sequential resonance of multiple linked or unlinked closed geometries across the network as a whole. This global resonance process gives rise to an intrinsic phenomenological property termed innergence, which characterizes the first-person experiential aspect of resonant state space identities. RCNNG thus distinguishes between the physical formation of closed neural geometries and their resonant identities, providing a unified account of perceptual stability, memory recall, reactivation of sensory experiences, and the emergence of conscious experience.
Category: Mind Science
[1703] ai.viXra.org:2607.0079 [pdf] submitted on 2026-07-28 08:51:36
Authors: Hasan Niazi
Comments: 27 pages, English. Copyright: CC BY 4.0.
The Resonance of Closed Neural Network Geometries (RCNNG) hypothesis proposes that perception, cognition, and conscious experience arise from the formation, resonance, and interaction of closed geometrical structures within neural networks. The original RCNNG preprint introduced the foundational principles of closed neural geometries, resonance dynamics, and associative linkage cite{Niazi2026RCNNG}. Building on that foundation, the present article extends the RCNNG framework by applying its core mechanisms to a broad range of perceptual, cognitive, and phenomenological phenomena. Using RCNNG as a unified explanatory model, this work analyzes basic and composite perception, conceptual reasoning, symbolic and mathematical abstraction, problem-solving, skill acquisition, memory formation, individual differences in recall, imagination, innovation, similarity and difference detection, logical bias, pre-perception and perception void, the distinction between perceiving absence and absence of perception, conscious experience and qualia, sensory processing, spatial navigation, sleep, free will, conditioned behavior, déjà vu, phantom limb experience, and several additional phenomena. Each phenomenon is interpreted through variations in the formation, resonance, linkage, and activation of closed neural geometries shaped by sensory input, internal dynamics, and prior experience. The analysis demonstrates that many seemingly unrelated cognitive and perceptual processes share a common geometric—resonance structure. By providing a single underlying mechanism for diverse phenomena, RCNNG offers a unified theoretical framework for understanding the architecture of perception, cognition, and conscious experience, and establishes a foundation for future theoretical and empirical development.
Category: Mind Science
[1702] ai.viXra.org:2607.0078 [pdf] submitted on 2026-07-28 13:19:32
Authors: Lluis Eriksson
Comments: 9 pages. Lean 4 / mathlib formalization; full core build 8422 jobs, 2431 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
A mass gap is a statement about the spectrum of an operator, but a latticegauge theory is given as a measure. The passage between the two - theOsterwalder-Seiler reconstruction - proceeds through reflection positivity, aGelfand-Naimark-Segal space, a transfer operator, and an identification theoremasserting that expectations in the measure are matrix elements of thatoperator. This paper reports a complete formal verification of that passage, inLean 4 with mathlib, for the Z_2 lattice gauge chain: from the Boltzmann weightexp(beta s) to exponential decay of a correlation function of the measure, withevery arrow a machine-checked theorem and no arrow assumed. The endpoint is theexact identity E_n[f(sigma_0) f(sigma_n)] = (tanh beta)^n for the signobservable, a statement in which no operator occurs and whose proof goes throughone, and whose rate is exactly the verified non-vacuum transfer eigenvaluetanh beta; equivalently, the normalised transfer operator has spectral gap1 - tanh beta > 0, and the corresponding mass is -log(tanh beta) > 0 forbeta > 0. All three are machine-checked.We state the limits with the same precision as the results. The system has oneZ_2 variable per time slice, so its spatial slice is a point and its transferoperator is a 2x2 matrix; a lattice with spatial extent is not treated. Thebound is at fixed finite size and is NOT volume-uniform. The pairing of thissystem is definite - proved, not assumed - so the Gelfand-Naimark-Segalquotient is the identity and therefore does no work; a system with a degeneratepairing still needs it. The underlying mathematics is textbook:Osterwalder-Seiler is from 1978 and the transfer matrix of the Ising chain isolder still. The contribution claimed here is not a new theorem but a verifiedcomposition: that the interfaces of the reconstruction fit together with nothinghidden between them, exhibited on the smallest system where all of them aresimultaneously present. Nothing in this paper is a claim about SU(N), thecontinuum limit, or the Yang-Mills mass gap.
Category: Mathematical Physics
[1701] ai.viXra.org:2607.0077 [pdf] submitted on 2026-07-28 20:35:35
Authors: Mohammed chanoufi
Comments: 3 Pages.
This paper introduces a novel cosmological framework named the "Fabric Displacement Model (FDM)". We conjecture that mass does not warp or contract spacetime curvature inwardly as described by standard general relativity; rather, mass exhibits an inherent geometric repulsion that locally displaces the cosmic spacetime fabric outwardly. By defining a localized "Fabric Density Gradient" ($ho_{text{fabric}}$), we show that the displaced cosmic fabric from galactic cores accumulates at galactic fringes, generating a high-density stabilization zone. Applying this framework to the flat rotation curves of galaxies, we derive a comprehensive dynamic model that eliminates the necessity for non-baryonic Dark Matter. The resulting velocity profiles naturally recover the empirical Modified Newtonian Dynamics (MOND) scaling law ($V^4 propto GM$) as a direct consequence of fluid-like spacetime conservation laws.
Category: Relativity and Cosmology
[1700] ai.viXra.org:2607.0076 [pdf] submitted on 2026-07-28 17:10:48
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8423 jobs, 2460 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
The Osterwalder-Seiler reconstruction passes from a reflection-positive measureto a Hilbert space by quotienting out the null space of the reflected pairing.In a companion development that step was present but did nothing: the pairingthere was definite, so the quotient was the identity, and that paper says so inits own abstract. This paper supplies the missing case, in Lean 4 with mathlib.For the Z_2 lattice gauge chain we take half-space observables of two timeslices - a four-dimensional space - and form the reflected pairing directly fromthe Boltzmann weights. For beta > 0 the reconstructed physical space istwo-dimensional. Integrating out the future collapses four observables onto twostates, and that collapse is the null space. We prove: the pairing factors through anindependently defined reconstruction map Phi; its self-pairing rearranges into amanifest sum of two non-negative terms, from which positivity and the null spacefollow together; the null space is EXACTLY ker Phi, not merely non-empty; anexplicit non-zero observable lies in it; and the quotient is isomorphic to thephysical space BY THE MAP Phi ITSELF, not by a dimension count.The degeneracy is the mechanism the reconstruction exists to handle, and the oneexpected to reappear in systems with larger half-space algebras. What is notclaimed: this is twotime slices and not m; still Z_2, one variable per slice, fixed finite size, andnot volume-uniform; Z_N for N > 2 is untouched; and the completion step of thereconstruction is trivial here because every space in sight isfinite-dimensional, which we state rather than present as work done. Nothing inthis paper is a claim about SU(N), the continuum limit, or the Yang-Mills massgap.
Category: Mathematical Physics
[1699] ai.viXra.org:2607.0075 [pdf] submitted on 2026-07-28 19:17:42
Authors: Lluis Eriksson
Comments: 6 pages. Lean 4 / mathlib formalization; full core build 8424 jobs, 2481 oracle commands, axiom set exactly {propext, Quot.sound, Classical.choice}, zero sorry and zero project axioms. All verification links anchored at a fixed commit.
Two companion developments verified an Osterwalder-Seiler reconstruction end toend for a lattice gauge chain whose spatial slice is a single point. Every stepof that chain begins by knowing the vacuum, and in the one-dimensional case thevacuum is free: the normalised transfer kernel has constant row sums, so theuniform vector is fixed, and T*Omega = Omega follows from normalisation alone.This paper asks what survives when the slice acquires spatial extent, andanswers in Lean 4 with mathlib.The algebraic half survives untouched. With time bonds only, the row sums of thetransfer kernel are constant for every spatial extent L, so the uniform vacuumpersists on a space of dimension 2^L; and the single-site sign observable is aneigenvector whose normalised eigenvalue is exactly tanh beta, with L free in thestatement.The uniform vacuum does not survive. Switching on a coupling between sites inside aslice makes the spatial weight depend only on the source configuration, so itfactors out of the sum over the target and the row sums becomeconfiguration-dependent. We exhibit two explicit configurations of a two-siteslice with different row sums, and conclude that no constant row sum exists: theuniform vector is not fixed, so T*Omega = Omega is FALSE for it. The vacuumbecomes a Perron vector that row-sum normalisation no longer supplies in closedform, and every later step of the reconstruction loses its starting point.We state plainly what the positive half is and is not. The decoupled system is Lnon-interacting copies of a two-state system, and the rate it yields - theeigenvalue tanh beta of the single-site sign mode - is independent of L fortrivial reasons, so it is physically empty and is recorded only because itisolates which half of the construction survives. NO GAP FOR THE COUPLED SYSTEM IS PROVED HERE, AND NONE IS CLAIMED.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.
Category: Mathematical Physics
[1698] ai.viXra.org:2607.0074 [pdf] submitted on 2026-07-28 01:09:59
Authors: Juan Nava Aroza
Comments: 2 Pages.
We present a unified cosmological modelstrictly framed in 3 + 1 spacetime dimensions based on the quantum dynamics of a non-Abelian gauge vector potential under the SU(2) symmetry group. By employing a Cosmic Triad configuration, we demonstrate that the field invariant exactly preserves macroscopic spatialisotropy, satisfying the stringent constraints of the Cosmic Microwave Background (CMB). At intermediate scales, the Savvidy quantum effective Lagrangian induces a self-regulated dynamic confinement (mass gap) that identically cancels both the effective pressure and the fluid’s sound speed (w = 0, c2s = 0), reproducing Cold Dark Matter (CDM) phenomenology without requiring exotic particlesor disrupting galaxy formation. In the late infrared limit, the freezing of the chromomagnetic vacuum naturally fixesthe equation of state at the Cosmic Constant boundary (w = −1). Finally, we show that the restoration of Conformal Invariance in extreme energy regimes, governed by the field’s Asymptotic Freedom, resolves the rigid scaleproblem in Penrose’s Conformal Cyclic Cosmology (CCC), offering a consistent physical mechanism for the analytical transition between eons.
Category: Relativity and Cosmology
[1697] ai.viXra.org:2607.0073 [pdf] submitted on 2026-07-27 21:33:38
Authors: Lluis Eriksson
Comments: 6 pages. All results machine-checked in Lean 4 (toolchain v4.29.0-rc6) against Mathlib pinned to commit 07642720480157414db592fa85b626dafb71355b; no sorry and no project axioms.
We machine-check, in Lean 4 with no sorry and no project axioms, theOsterwalder-Seiler reflection positivity of a lattice gauge theory with finiteabelian gauge group. The development is organised so that the three ingredientsare separated and each is proved on its own: an analytic step, a geometric step,and the single place where a property of the Boltzmann factor is actually used.The analytic step is that a crossing kernel of the formK(x,y) = sum_i c_i phi_i(x) conj(phi_i(y)) with c_i >= 0 is positivesemidefinite, that this class is closed under products, and that it is closedunder conjugation by a positive diagonal. Formulating the hypothesis as anon-negative combination of characters rather than as non-negativity of Fouriercoefficients removes any need for Bochner's theorem on a finite abelian groupand for the Schur product theorem: the development uses no spectral and nomatrix-positivity API.The geometric step is a splitting of the configuration space across thereflection plane under which the reflection is the swap and the Gibbs weightfactors as w(x) w(y) K(x,y). We prove that the Osterwalder-Seiler pairing of anobservable of one half against its reflection is then exactly the quadratic formof w(x) K(x,y) w(y), so that reflection positivity follows from the analyticstep.The physical step is the instance. For Z_2 the Wilson factor exp(beta s),s = +-1, expands in the two characters with coefficients(exp(beta) +- exp(-beta))/2, both non-negative exactly when beta >= 0; so theZ_2 Wilson crossing kernel is positive semidefinite at non-negative coupling. Asingle endpoint combines a gauge system with a nontrivial time reflection, aconcrete splitting, that weight at positive coupling, and the conclusion; itsplaquette straddles the reflection plane, so the entire Gibbs weight is thecrossing kernel. It is a two-edge system, and a full temporal box is nottreated. For Z_N with N > 2 the coefficients are discrete Bessel-type sums andtheir non-negativity is not established here.We are explicit about what is absent: no Gelfand-Naimark-Segal quotient, notransfer operator, no identification of a Euclidean correlator with a matrixelement, and therefore no mass gap. Nothing here is a claim about SU(N), thecontinuum limit, or the Clay problem.
Category: Mathematical Physics
[1696] ai.viXra.org:2607.0072 [pdf] submitted on 2026-07-27 08:08:11
Authors: Veaceslav Molodiuc
Comments: 8 pages. AI-assisted preprint, Version 1.1.
Verified distributed kernels require more than authenticated messages: they require formal identity, recoverable operational states, and measurable consensus risk. This paper connects formal identity, discrete stabilization, the LoculoSoft kernel vocabulary, and PRISM probabilistic model checking. LoculoSoft is treated cautiously as a proposed structural framework and research direction. A reproducible PRISM 4.10.1 check on a three-process Herman-style token ring shows stable reachability with probability 1 and maximum expected stabilization time near 4/3 steps.Keywords: formal identity, discrete stabilization, consensus risk, distributed kernels, PRISM, LoculoSoft.
Category: Artificial Intelligence
[1695] ai.viXra.org:2607.0071 [pdf] submitted on 2026-07-27 20:37:30
Authors: P. H. Antom
Comments: 28 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
The climate is not one system but a system of systems: dynamical processes nested inside dynamical processes, each layer stable on its own terms and each layer coupled to the ones above and below it. This paper sets out that nested view formally — dynamical system → complex adaptive system (CAS) → panarchy of CAS across scale, with both its spatial half (nested scale) and its temporal half (Holling's adaptive cycle, and the cross-scale "revolt" and "remember" connections that couple fast and slow cycles together) — and then builds outward from theory toward derivation, detection, and evidence. A real, historically-published bistable climate model (Stommel, 1961) is worked through analytically as well as numerically: the smooth saddle-node fold at the top of its bistable window is confirmed symbolically via det(J)=0, while the transition at the bottom is shown to be a qualitatively different mechanism — a border-collision bifurcation at the model's own non-smooth |T−S| kink, occurring at the exact closed form η2 =η1η3, not a mirror-image fold, and confirmed to survive smoothing of that kink rather than being an artifact of it. The rise in variance and autocorrelation before a tipping point is derived from the model's linearized dynamics (an Ornstein—Uhlenbeck approximation whose leading eigenvalue is the same quantity that vanishes at the fold), and that derivation is checked against simulation: the autocorrelation prediction matches at r=0.86, and the variance prediction reveals a genuine second-order lag effect explained by the same slowing-down it is trying to detect. The noise-induced tipping mechanism is given its classical Kramers rate, tested by direct Monte Carlo simulation and confirmed by a Kolmogorov—Smirnov test on the escape-time distribution; its rate-induced counterpart is tested across four independent setups (symmetric and asymmetric potentials, single-variable and coupled systems, pulses and one-way ramps) for a genuine jump — none found — a real, structurally-characterized negative result rather than a gap left unexamined. A fifth test asks the natural remaining question directly: combining sub-threshold noise with a one-way ramp produces a sharp, real rise in tipping probability as the ramp slows, the opposite direction from deterministic intuition, and this is shown to require no new mechanism at all, being fully predicted by integrating the paper's own Kramers rate over the ramp's shrinking barrier — exposure time, not rate, is the operative quantity. (Trnucated by ai.viXra.aorg Admin to < 400 words)
Category: General Science and Philosophy
[1694] ai.viXra.org:2607.0070 [pdf] submitted on 2026-07-27 16:38:14
Authors: Lluis Eriksson
Comments: 8 pages. All results machine-checked in Lean 4 (toolchain v4.29.0-rc6) against Mathlib pinned to commit 07642720480157414db592fa85b626dafb71355b; no sorry and no project axioms. Source modules, axiom-oracle transcripts and a theorem-to-artifact map are hy
Inside a Lean 4 formalization programme for four-dimensional SU(N_c) latticeYang-Mills, we machine-check the operator-theoretic criterion that standsbetween exponential decay of a Euclidean correlator and a spectral gap of atransfer operator. Let T be a bounded self-adjoint operator on a Hilbert spaceand W a unit vector fixed by T, so that TW = W, and put S = T - |W><W|.Exponential decay at rate r of the connected two-point function<v, T^n v> - |<W,v>|^2 at every v is equivalent to the operator-norm bound||S|| <= r.The substantive part is the dense-family criterion. WritingD_r = {v : there is C with ||S^n v|| <= C r^n for all n}, we prove that D_r isa linear subspace and that its density alone forces ||S|| <= r, the constantsbeing entirely unconstrained: a family of observables whose span is dense, eachcarrying its own finite constant, suffices. Consequently prefactors that growwith the support of the observable - the shape cluster expansions produce - donot obstruct the gap, provided the exponential rate is common to the family andthe family spans densely. Those two provisos are essential; without them thestatement is false.No mathematical novelty is claimed for the criterion itself, which we expect tobe known in the language of local spectral theory; what is offered is itsmechanization, its packaging for families of observables, and the consequencefor prefactors. We also record what the formalization does not contain: noOsterwalder-Seiler Hilbert space for any gauge theory, no reflection positivityof the Wilson measure, no identification of a Euclidean correlator with a matrixelement. Nothing here is a claim about the continuum limit or about the Clayproblem. All results are machine-checked with no sorry and no project axioms. (W stands for the vacuum vector Omega. If the form's preview renders Unicode cleanly you may substitute the real symbols; the ASCII form above is the safe default and matches the PDF's content either way.)
Category: Mathematical Physics
[1693] ai.viXra.org:2607.0067 [pdf] submitted on 2026-07-27 02:10:37
Authors: Michael Quigley
Comments: 149 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This forensic engineering audit formally dismantles the non-predictive "Abstract Curtain" of 20th-century physics, replacing mathematical phantoms with the industrial hardware of a 10²² kg/m³ Rigid-Packed Plenum (The Universal Marble Pit). We formally dismiss the model of "photons as bullets"—which succumb to the Dispersal Paradox at terminal densities—reclassifying light as the discrete mechanical "Sound of Gears Clicking". In doing so, we validate Albert Einstein’s 1954 confession that theories without a physical medium are merely "castles in the air".Physical reality is established as a singular, phase-locked instrument initiated by the Big Roar (Rudra) and driven by a 13.33 Hz (800 RPM) "Bridegroom" Motor. Sustained by the Ethos-648 Monobrick (Autonomous Standing Wave Generator), the framework resolves the Wait-Time Paradox; matter "stands up" locally and simultaneously across the machine via Stadium Wave Logic. Consequently, we replace Einstein’s E=mc2 with the Universal Seesaw Identity (E=mΦ), reclassifying the speed of light as Lattice Setup Time (Lu209b)—the mechanical "Wait-Time" required for the motor to compress elastic "marshmallow" gaps and achieve Zero-Point Solidity.This transition mandates a 1.35 Expansion Ratio for stable 3D rotation and unmasks the Fine Structure Constant (1/137.036) as the mandatory Volumetric Slip-Ratio for gear-clearance. We anchor the gearbox to the 34.5 Trillion Kilometre Terminal Acoustic Horizon (137-Wall), dictating a maximum setup delay of 4.15 to 4.25 years. This unmasks the 13.8-billion-year age of the universe as a friction-based metrological error, providing the industrial blueprint for an LHC Phase-II Upgrade via Resonant Docking, unlocking a new era of Universal Abundance and biological re-tuning
Category: Quantum Physics
[1692] ai.viXra.org:2607.0066 [pdf] submitted on 2026-07-27 02:08:39
Authors: Michael Quigley
Comments: 37 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This engineering manual formally dismantles the "Abstract Curtain" of expansion-based cosmology, reclassifying physical reality as a singular, phase-locked instrument driven by SOUND—the single and only force in the cosmos. We replace the failures of General Relativity with the Tychosian Hub, a geo-heliocentric gearbox where a Stationary Earth-Axle serves as the thermodynamic mandate for planetary survival in a 10²² kg/m³ Rigid Plenum. We provide the hardware receipts for Stellar Vaporization, unmasking solar heat as a friction-based odometer of the Sun’s orbital velocity.The centerpiece of this mandate is the Universal Seesaw (E=mΦ), which restores instantaneous conduction at Time-Zero via the 1D Snooker Cue effect. We formally identify Jupiter and Saturn as superconducting LMH Shield Fans that protect the terrestrial hub, while providing the 337/227 Pineapple Proof as biological verification of the universal motor’s Fibonacci exhaust. By applying the 42,000x Scale Correction and the 0.472° Precession Delta, we reveal a compact, perpetual machine where celestial bodies are parked in Fibonacci Nodal Slots and governed by the 13.5 macro-gearing resultant
Category: Quantum Physics
[1691] ai.viXra.org:2607.0065 [pdf] submitted on 2026-07-27 02:07:27
Authors: Michael Quigley
Comments: 82 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This engineering manual formally dismantles the "Abstract Curtain" of expansion-based cosmology and probability-cloud chemistry by reclassifying physical reality from an empty void into a measure of Acoustic Work performed across a 1022 kg/m3 Rigid-Packed Plenum. We move beyond the non-predictive "Maths-Magic" and systemic failures of the Standard Model (SM) to establish the Master Ledger of Nodal Slots, unifying sub-atomic, planetary, and cosmological scales through the Marshmallow Squeeze (Cu2098)—the physical compression of elastic inter-granule gaps required to achieve Zero-Point Solidity.Crucially, this audit performs a Terminal Metrological Rectification of the Planck Length (1.6×10−35 m). By reclassifying this value as Acoustic Interaction Lag (the infinitesimal "shiver" between gears), we identify the actual physical building block—the Ether Granule—as being 23 orders of magnitude larger (1 picometre) than standard theory assumes. This correction resolves the "Infinity Problem" inherent in treating particles as dimensionless points and proves that mass and distance are deterministic results of hardware assembly rather than mathematical phantoms.Building upon the wave-center blueprints of Energy Wave Theory (EWT), we identify the Ethos-648 Monobrick (Golden Coordinate) as an Autonomous Standing Wave Generator (AWG) that stabilizes vibrations into deterministic Fibonacci Record Grooves, providing the mandatory gear-clearance required for rotation without shattering against the plenum’s back-pressure. We formally reclassify magnetism from an abstract vector field into a physical Directional Ether Wind pumped by trillions of sub-atomic volcanoes (centrifugal pumps). We define the dual operational modes of the electron: Mode A (Static Girder) providing 1D axial rigidity via Sigma-bonded "Hurricane Stacks," and Mode B (Dynamic Current) where electrons function as spinning "bicycle wheels". We identify the 720-degree spinor reset as a periodic "Hairdryer Exhaust" (side-kick) that forces currents into the corkscrew S-shapes observed in Birkeland filaments, providing the deterministic mechanical cause for the geometry of the Electric Universe.We validate the 84.4 pm Blueprint Width and the 10π Geometric Snap (31.4 pm), proving with 99.9% forensic accuracy that the measured Bohr Radius (52.9 pm) is the hardware resultant of the work required for spherical closure within a rigid medium. This logic fractals upward to the Tychosian Hub, identifying the Moon as the macroscopic mirror of the Hydrogen 1s orbital and planetary orbits as Physical Record Grooves carved into the plenum by the 813.3 Hz master pulse. We provide the hardware receipts for Stellar Vaporization, unmasking solar heat as a friction-based odometer of the Sun’s orbital velocity, and restore Earth-stationarity as a thermodynamic mandate; the Vaporization Proof confirms that any orbital speed through the 1022 plenum above 1 mph would vaporize the planetary crust into plasma instantly.The centerpiece of this mandate is the Universal Seesaw (E=mΦ), which restores instantaneous conduction at Time-Zero via the 1D Snooker Cue effect. Perceived light-speed is reclassified as Lattice Setup Time (Lu209b)—the mechanical "Wait-Time in the Lobby" required for the 13.33 Hz universal motor to engage the Acoustic Clutch and squash the elastic "marshmallow" gaps flat. This provides the singular mechanical explanation for Quantum Entanglement and Instantaneous Action-at-a-Distance, reclassifying entangled states as wave-centers physically sharing the same rigid mechanical rod.Finally, we dismantle the "Expansion Speedometer" by reclassifying Redshift (z) as a Cosmological Torsional Odometer (z=zu2081+nzu2082+zu2083), measuring the mechanical "groan" and bit-rate loss of a signal navigating trillions of elastic buffers. By applying the 42,000x Tychosian Correction and reclassifying space as a solid-state Geoaxial Motor where magnetism is induced by celestial rotors, we reveal a compact, phase-locked gearbox operating on a Tilted Floor and bounded by the 34.5 Trillion Km Terminal 137-Wall (Hubble Limit). With the Pineapple Proof and the precision machining of glucose providing biological verification of the universal motor’s Fibonacci exhaust, this audit initiates the handover to the Toolmaker’s Apprentice. We are no longer accidental witnesses to "castles in the air"; we are now in possession of the Engineering Service Manual for an eternal instrument operating in the Now
Category: Quantum Physics
[1690] ai.viXra.org:2607.0064 [pdf] submitted on 2026-07-27 02:06:12
Authors: Michael Quigley
Comments: 114 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
ABSTRACT: THE FORENSIC INDICTMENTThis paper serves as the final Forensic Indictment of 20th-century 'maths-magic,' specifically dismissing the non-predictive Higgs field and expansion fables. We formally validate Albert Einstein’s 1954 confession that medium-less theories are merely "castles in the air," reclassifying abstract "fields" into deterministic industrial resultants machined within a diamond-hard, 10²² kg/m³ Rigid Plenum. We provide the Indestructible Industrial Ledger for the R.U.T. WSM framework, presenting 27 trilateral audit tables that contrast Standard Model (SM) fudges with deterministic hardware. The centerpiece of this audit is the Trilateral Magnitude Match, which proves that terrestrial laboratory force (Ampère’s Law) is the direct resultant of the synchronized 1-3-6 Electron Peloton strike.We formally document the Eight-Rung Resonant Ladder required to bridge macroscopic ignition to sub-atomic power, along with the Triple-Lock 1836 Mass-Ratio and the Torsional Friction Odometer. By anchoring the framework to the 2008 Lund University attosecond film, we provide the visual "Check-Mate" for the composite nature of matter and the 1/137 Volumetric Slip-Ratio. We unmask 'star formation' peaks in the Madau Plot as industrial thresholds of gear-stress and verify the gearbox’s stationary axle via the 8.2 km/s Seismic Odometer. Anchoring the cosmos to the 34.5 Trillion Km Terminal 137-Wall via the 42,000x Tychosian Correction, this manual directs the transition from the "Stochastic Ballistics" of smashing gears to the Resonant Docking of driving them. This manual offers the Toolmaker’s Apprentice the terminal data shields required to drive the machine of the stars in the eternal Now.
Category: Quantum Physics
[1689] ai.viXra.org:2607.0063 [pdf] submitted on 2026-07-26 22:54:26
Authors: Yaakov Abdelhak
Comments: 3 Pages.
We investigate the integer solutions of the Diophantine relation = for non- square integers when n> 2. By projecting parameters and as the functional side lengths of a variable geometric boundary, we leverage the Law of Cosines (LOC) to track rational and irrational distributions. Using the integer constraints inherent to Fermat's hypothesis, we demonstrate a structural field mismatch under acute angular transformations, bypassing perfect square integers handled via classical infinite descent.
Category: Number Theory
[1688] ai.viXra.org:2607.0062 [pdf] submitted on 2026-07-24 11:56:06
Authors: R. Minamoto
Comments: 4 Pages.
We establish a rigorous, non-equilibrium thermodynamic framework governing the dynamic reconstruction of bulk spacetime geometry from boundary quantum states within the AdS/CFT correspondence. Adopting a phenomenological toy-model approach, we bypass the microscopic ultraviolet (UV) complications to extract universal constraints on holographic processing. Utilizing the Complexity=Action (CA) conjecture, we model the temporal evolution of emergent bulk geometry as a manifestation of unitary quantum gates. By extending the generalized Landauer principle to the quantum regime, we derive the unavoidable entropy production rate ($dot{S}_{text{gen}}$) triggered by irreversible state transitions at the boundary. Incorporating this dissipative channel into the extended first law of black hole thermodynamics, we compute the explicit gravitational backreaction on the bulk geometry using a 3D BTZ black hole background. We prove that a holographic quantum rendering efficiency ($eta_{text{hq}}$) naturally emerges and vanishes as the computational rate saturates the fundamental Lloyd's bound. This dynamic constraint establishes an absolute upper bound on the Hawking temperature ($T_{text{H}}$), forcing a finite-time geometric divergence at $t_{text{crash}}$. Rather than a mere destruction of information, we show that this critical threshold triggers a topological phase transition, serving as a non-local birth mechanism for parallel spacetime domains within a holographic multiverse.
Category: Quantum Gravity and String Theory
[1687] ai.viXra.org:2607.0061 [pdf] submitted on 2026-07-24 22:05:48
Authors: Ertuğrul Karakaplan
Comments: 6 Pages. 1 figure. AI-assisted scholarly e-print.
While the standard ΛCDM model successfully describes an accelerating universe, treating Dark Energy (DE) and Cold Dark Matter (CDM) as non-interacting entities leaves the ultimate geometric and thermodynamic fate of the cosmos unresolved. Building upon interacting dark fluid models (such as the generalized Chaplygin gas) and multiply-connected topologies, this paper proposes a unified mechanical framework for a universe with a toroidal ({mathbb{T}}^{3}) geometry. I hypothesize that continuous isotropic expansion exerts escalating volumetric strain on the spacetime continuum, forcing the central hyperspace void of the torus to contract. As this geometry approaches a forced topological phase transition from a genus-1 to a genus-0 state, the resulting topological stress reaches a critical threshold. I argue that this threshold disrupts the phase equilibrium between DE and DM, halting their conversion. The inability of the metric tensor to smoothly seal the central void culminates in localized spacetime ruptures—a Topological Big Rip. Consequently, the rapid disintegration of the Dark Matter scaffold leads to the gravitational decoupling of baryonic structures, subjecting visible matter to viscous macroscopic dissolution and localized collapse in a torn continuum.
Category: Relativity and Cosmology
[1686] ai.viXra.org:2607.0060 [pdf] submitted on 2026-07-25 07:45:13
Authors: Bing Zhang
Comments: 11 pages, 2 figures, 29 references. AI-assisted research
The graviton is a hypothetical particle of modern physics that has yet to be directly detected.Mainstream theories (string theory, loop quantum gravity) assume the graviton is a fundamentalparticle. This paper proposes an alternative hypothesis based on complex adaptive system (CAS)emergence theory: the graviton is not a fundamental particle, but rather an emergent phenomenonarising from the collective quadrupole excitations of nucleons (and deeper quark—gluon degrees offreedom) within atomic nuclei in the long-wavelength limit—analogous to phonons being quantizedlattice vibrations.We establish a three-scale theoretical framework (quark—nucleon—nucleus) and verify the mathematical structure of the conjecture through numerical simulations in simplified 3D lattice models:nucleon collective quadrupole oscillations naturally possess spin-2 character, and their mass tends toward zero in the long-wavelength limit. This conjecture bridges the "scale gap" between Sakharov’sinduced gravity (1967) and Verlinde’s entropic gravity (2011)—providing a concrete microscopicmechanism for emergent gravity.We present three independent numerical approaches (static Hessian diagonalization, QCD-inspiredbag model, and molecular dynamics time evolution) that converge on the existence of intrinsic lowenergy spin-2 collective excitations in nuclear matter with ω ∼ 0.6—2.0 MeV. We discuss the relationship with the fractional quantum Hall (FQH) emergent graviton, the Weinberg—Witten theoremand four pathways around it, and propose three experimentally testable predictions accessible withcurrent nuclear physics facilities.
Category: Quantum Gravity and String Theory
[1685] ai.viXra.org:2607.0059 [pdf] submitted on 2026-07-25 22:33:11
Authors: Ertuğrul Karakaplan
Comments: 4 Pages.
While standard cosmological models frequently treat the Dark Sector as a non-dissipative background, the morphological duality of the universe—manifesting as spherically symmetric structures (e.g., stellar systems and dark matter halos) versus rotation-dominated vortices (e.g., spiral galaxies and black hole accretion disks)—demands a more comprehensive fluid-dynamical treatment. Building upon the framework of interacting dark fluids and topological stress, this paper investigates the dual mechanical behavior of a viscous Dark Sector. I hypothesize that isotropic volumetric components of the dark fluid act as a global confining pressure, driving the hydrostatic equilibrium necessary for spherical symmetry, while localized shear stresses and angular momentum transfer generate rotational vorticity. By applying continuum mechanics and Navier-Stokes analogies to cosmic scales, I propose a unified morphological framework that explains how distinct stress regimes dictate the geometry of cosmic structures.
Category: Relativity and Cosmology
[1684] ai.viXra.org:2607.0058 [pdf] submitted on 2026-07-23 06:20:48
Authors: Jason Merwin
Comments: 8 Pages. Links to the repository are locked Zenodo releases are provided
We present pre-registered, cryptographically frozen structural predictions for CMS Run-3 dijet angular distributions (1/σ) dσ/dχ at 13.6 TeV, derived from the Discrete Emergent Universe (DEU) computational framework. Under a single published energy anchor (E24 ↔ 6.14 TeV) and a two-stage pre-registration protocol frozen before any profiling simulation existed, the model predicts: a pre-boundary excess accumulating at 1 < χ < 2 with a soft-wall deficit immediately above χ = 2 in the 7—8 TeV dijet mass bin; and, above 8 TeV, an inversion of the post-boundary deficit to a weak excess as the boundary softens and leaks, with the negative step S∗ and edge-log-drop ∆∗ persisting in both bins. All prediction values trace through SHA-256 hashes to simulation instruments certified row-exact against the archived output of the original DEU collision campaign. We additionally report the profiling ladder beyond the scored range, which exhibits a previously uncharacterized regime of simultaneous channel extinction, and an exploratory analysis of collision phenomenology versus foam age whose central qualitative claims are shown to be robust across a declared band of instrument-reconstruction uncertainties. Negative results obtained during the campaign are documented with the same prominence as positive findings.
Category: High Energy Particle Physics
[1683] ai.viXra.org:2607.0057 [pdf] submitted on 2026-07-23 11:31:51
Authors: Tomasz Kobierzycki
Comments: 31 Pages.
This work asks what is obtained when the observer-independent light cone isused to organise the complete orientation of a local clock--ruler frame, ratherthan only the ordinary future-timelike part of that orientation. The result isa four-sector description of one spacetime. The sectors are not paralleluniverses and do not provide four independent metrics. They are the foursuccessive orientations met when a local time axis, a spatial axis, theopposite time axis, and the opposite spatial axis are followed around oneextended Lorentz orbit.The same distinction is applied separately to matter and geometry. A particlehas a fixed sector relative to the local geometric frame and undergoes ordinaryLorentz boosts only inside that sector; it is never accelerated through thelight boundary into another particle class. Curved geometry may insteadrequire a neighbouring sector chart when one of its proper scales reaches anull limit. A tensorial scale construction identifies the affected direction,pairs it with the local clock, and replaces the failed extrapolation by thereciprocal scale of the adjacent chart while retaining the samegeneral-relativistic solution.In Schwarzschild, LTB, Kerr, and FLRW geometries this procedure turns theapparent zero of an inactive scale into an infinite proper scale measured fromthe neighbouring sector centre. Curvature regularity is then a result to bechecked with invariant scalars, not an effect assigned to a tetrad rotation.Because every sector is a reading of one geometry and one field history, thesame framework also constrains black--white-hole interpretations, cosmologicaltime reversal, and closed timelike curves. The construction is presented as acoherent classical framework whose remaining dynamical and quantum conditionsare stated explicitly.
Category: Relativity and Cosmology
[1682] ai.viXra.org:2607.0056 [pdf] submitted on 2026-07-22 10:12:44
Authors: Brent Hartshorn
Comments: 25 Pages.
Dorau and Much (2026) [1] have shown, using Tomita—Takesaki modular theory, that the Araki—Uhlmann relative entropy between the vacuum and a coherent excitation of a scalar field on a local Rindler horizon equals the boost-energy flux across the horizon, and that the semi-classical Einstein equations follow once this relative entropy is identified with one quarter of the horizon area variation. Two limitations remain: the Rindler bifurcation surface has infinite area, so only area variations are meaningful, and the derivation leaves open what the Bekenstein—Hawking normalization S rel = δA/4 is counting. We address both by transplanting the construction from the local Rindler wedge to the Nariai spacetime dS2 × S 2 , the degenerate limit of Schwarzschild—de Sitter in which the black-hole and cosmological horizons coincide.Nariai possesses a global bifurcate Killing horizon with a compact bifurcation surface of area A = 4π/Λ, so every quantity in the derivation — the horizon two-point function, the modular flow, the relative entropy, and the total area — is finite. We compute the relative entropy for coherent excitations on the Nariai horizon — exhibiting the modular Hamiltonian explicitly, factorizing the transverse sphere out of the Araki—Uhlmann formula mode by mode, and evaluating the entropy in closed form for an explicit family of s-wave excitations — and verify that the identification S rel = δA/4 reproduces the Einstein coupling α = 8π with no infinite-area subtraction. The linear-response model through which the area variation enters — the one postulate of the flat-space derivation — is here derived rather than assumed: the s-wave back-reaction of the throat is exactly linearized de Sitter Jackiw—Teitelboim gravity, whose dilaton equation admits the response model as its unique zero-mode-free solution, with the coupling 8π fixed by the dimensional reduction.Because the Nariai background is itself unstable to vacuum polarization, we quantify the domain of validity of the equilibrium construction: the Ginsparg—Perry/Bousso—Hawking instability evolves at a rate suppressed relative to the modular frequency by the inverse horizon entropy, Γ/κ ∼ 1/SN , so the Kubo—Martin—Schwinger structure holds as a quasi-equilibrium over ∼ SN thermal times — self-consistent at precisely the order at which the semiclassical Einstein equations are derived.
Category: Quantum Gravity and String Theory
[1681] ai.viXra.org:2607.0055 [pdf] submitted on 2026-07-22 22:01:16
Authors: Carl Max Reed
Comments: 2 Pages.
In the Williamson-van der Mark electron model [1], the electron is not an abstract, zero-dimensional mathematical point particle possessing an unexplainable monopoly of negative charge. It is a highly localized, three-dimensional toroidal electromagnetic photon vortex spinning at the fundamental Planck scale. Concurrently, Planck's constant (h) is not an arbitrary, ungrounded cosmic decree injected into reality from an external container; it is the direct, invariant geometric boundary condition required for the stability of a continuous, self-confined wave loop within a non-linear electromagnetic fluid substrate [2].
Category: Mathematical Physics
[1680] ai.viXra.org:2607.0054 [pdf] submitted on 2026-07-22 22:00:37
Authors: Carl Max Reed
Comments: 3 Pages.
This paper presents a non-dual, polycentric cosmological paradigm that eliminates the artificial dualisms between empty space, discrete point-particles, and independent fundamental forces. We mathematically and philosophically establish that the physical vacuum medium is nothing other than the Electromagnetic (EM) energy field itself at itsbase state. Material reality, forces, and conscious experience are established not as independent entities, but as topological, refractive, or phase-resonant states of this single, self-perceiving EM ocean. By synthesizing Henri Poincaré’s prior equation of inertia (m = E / c^2) with Robert Dicke’s variable refractive index model of gravitation and E.T. Whittaker’s two underlying scalar potentials, this work provides concrete solutions to major foundational crises inphysics. Specifically, it eliminates the infinite self-energy paradox of the electron, provides a near-field electrodynamicmechanism for the nuclear forces, and accounts for flat galactic rotation curves without invoking the hypothetical construct of "dark matter".
Category: Mathematical Physics
[1679] ai.viXra.org:2607.0053 [pdf] submitted on 2026-07-21 23:30:13
Authors: Rüdiger Giesel
Comments: 47 Pages.
The Standard Model accounts for fermion masses through Yukawa couplings, but thenumerical values and hierarchical pattern of these couplings remain external inputs. Thisarticle develops a geometric octonionic framework in which fermion-mass hierarchies areencoded in the spectrum of a projected non-associative vacuum operator. The constructionstarts from three octonion-valued fields, whose associator is promoted to a dynamicalvacuum quantity. A master action is formulated, its non-associative vacuum equationsare reduced in a canonical sector, and an algebraically motivated symmetry-breakingterm is introduced through a preferred associative quaternionic subalgebra and a Fanooriented vacuum direction. The resulting structure defines a self-adjoint associator numberoperator and a geometric spectral mass operator. Four closure statements are formulated:vacuum-scale closure, associator spectral closure, projector normalization closure, andRG reconstruction closure. The main result is not a claim of experimentally proven exactfermion masses, but a mathematically explicit framework in which exact masses wouldfollow once four closure blocks are solved without additional phenomenological input: theabsolute octonionic vacuum scale, the exact associator Hessian spectrum, the projectornormalization of the fermion sectors, and the renormalization-group matching to measuredmass conventions. In the minimal Fano-plane vacuum, the linearized associator matrix isevaluated explicitly and yields the non-zero spectral levels 4,8,12, i.e. the normalizedgeneration skeleton N1 : N2 : N3 = 1 : 2 : 3. A charged-lepton benchmark then shows howthe same spectral template can reproduce the measured e,µ,τ hierarchy once the sectorinvariants are fixed. The paper therefore provides a controlled route from octonionicnon-associativity to fermion mass hierarchies and identifies the remaining mathematicalrequirements for a parameter-free mass prediction. In its final form the closure programis strengthened by an explicit full-Hessian decomposition, a projector-uniqueness theoremmodulo the vacuum stabilizer, a finite charged-lepton trace test, and a component-levelcontraction formula for the lepton Hessian moments that makes the no-fit criterionoperational before comparison with observed masses.
Category: High Energy Particle Physics
[1678] ai.viXra.org:2607.0052 [pdf] submitted on 2026-07-21 19:22:23
Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 155 Pages.
This book grew out of a short paper, Linguistics in the Time Cycle, in which we sketched a single conjecture: that language is not merely something that changes in time but something that is organised by time, across many nestedscales at once. The paper proposed an analogy—language as a temporally regulated system, parallel in its architecture to the way genetic information is expressed, regulated, and inherited through biological time. What began as a set of tables and suggestive parallels seemed to invite a fuller treatment. The present monograph is that treatment. The argument is interdisciplinary by necessity. To speak of language in time is to borrow at once from chronobiology and phonology, from populationgenetics and historical linguistics, from Bakhtin’s poetics of the chronotope andfrom the mathematics of dynamical systems. We have tried throughout to keep the analogy disciplined: an analogy is a scaffold for hypotheses, not a proof, and the value of the LTC framework lies in the concrete, testable questions it makes it natural to ask. Each chapter therefore closes by pointing toward empirical or computational work that could confirm or refute the picture it paints.
Category: Linguistics
[1677] ai.viXra.org:2607.0051 [pdf] submitted on 2026-07-21 17:44:48
Authors: Joerg Moesch
Comments: 27 Pages.
In this paper, the natural three-dimensional extension of the complex and dual numbers is introduced: the trinion algebras Y(k) of the form a+bi+cj with i²=-1, j²=0 and the commutative coupling ij=ji=k, where k = α+βi+γj is an element of the algebra. The family Y(k) is systematically investigated: multiplication, division and inverses are derived. Special attention is given to the phenomena induced by non-associativity, which lead to invertible zero divisors, non-unique division, and rich geometric structures. The eight fundamental algebras with α,β,γ ∈ {0,1} are examined and their zero divisor sets are visualized. Numerical examples for the algebra Y(1) illustrate the observed phenomena.
Category: Algebra
[1676] ai.viXra.org:2607.0050 [pdf] submitted on 2026-07-20 02:21:31
Authors: J. W. McGreevy
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)
We present a self-contained technical development of the reduced variational structureunderlying the Relativistic Field Theory of Primes (RFTP) in the weight-12 sector. AfterDirac reduction by the global valence constraint associated with the modular discriminant∆(τ ), the effective dynamics on the reduced space are generated by a convex action functional whose long-time minimizers are atomic measures supported at irregular primes. Weconstruct three explicit objects: (i) a linear isomorphism from the odd Galois eigenspacesfurnished by the Herbrand—Ribet theorem to local sections of the global spinor bundle, intertwining Galois action with Gauss—Manin parallel transport; (ii) a quantitative exponential convergence result for the Hopf—Lax semigroup showing that every admissible initial measure converges to a unique atomic minimizer at a rate controlled by the spectral gap of theHessian; and (iii) a term-by-term identification of the Weierstrass product of the regularizeddeterminant of the limiting operator with that of the completed Riemann xi function Ξ(s).These constructions render rigorous a four-step variational obstruction that selects discretearithmetic configurations whenever a continuous configuration would require an effective local exponent exceeding two. The entire development is phrased in the language of deterministic Hamilton—Jacobi—Bellman dynamics on a reduced symplectic manifold, thereby supplying both the analytic core of the weight-12 theory and the notational and conceptual bridge to a universal formulation over all weights.
Category: Mathematical Physics
[1675] ai.viXra.org:2607.0049 [pdf] submitted on 2026-07-18 18:19:27
Authors: Aaron Lee Alai
Comments: 16 Pages.
Bell derivations rest on locality, determinism, and measurement independence. Hall [2] pricedthe third assumption exactly for the singlet state: (√2 − 1)/3 ≈ 13.81% of measurementindependence must be surrendered for a local deterministic model to reproduce all singletcorrelations. We extend that program to multipartite stabilizer scenarios and compute theexact minimum measurement dependence required to reproduce the full faithful statistics ofGHZ/Mermin experiments — the optimal-model problem Hall posed and left open in 2011,having priced the tripartite perfect correlators alone at 1/3 [11]: F(3) = F(4) = 1/3, F(5) = F(6)= 2/5, F(7) = F(8) = 4/9, F(9) = F(10) = 8/17, F(11) = F(12) = 16/33, F(13) = 32/65 [LPEXACT, two-machine verified], with hand proofs at n = 3, 4; the reduction theorem showsthe faithfulness constraints are free, so Hall’s correlator-only tripartite threshold is promotedto the faithful value, and everything at n ≥ 4 is new. All eleven points obey the closed law F =R/(2(R+1)), with R = 2^⌊(n−1)/2⌋ the Mermin violation ratio [15]; a proven combinatoriallower bound (Theorem 5) is tight on every computed core and homogeneous family; and auniversal ceiling F ≤ 1/2 [PROVEN] shows the statistics never require totalsuperdeterminism — a faithful model surrendering no more than half exists at every size. Theoptimal hidden-variable densities have a closed physical form: uniform measures on thecontextual ground states of the prepared state’s frustrated stabilizer Hamiltonian — aninheritance principle confirmed out-of-sample on cluster states. The landscape is glassy(energy is spectral, supported on stabilizer characters) and provably beyond any pairwiseinteraction. We then pose the supply question as an open race: every published lawfulmeasurement-dependence program — invariant-set theory, cellular-automaton interpretations,future-input dynamics, all-at-once retrocausality, and the displacement-condensate frameworkof the present authors — is graded against this one answer key, steelmanned in its ownformalism, with several opening calculations executed here on rivals’ behalf. The condensatemechanism’s consolidated derivational debt is paid in-model: under exact U(1) conservationwith no external phase reference, a collective emission leaves a superselected two-branchrecord whose coherence support equals the prepared state’s stabilizer group, forcing theeffective energy’s term content to coincide with the required Hamiltonian’s — winding-ncoherence amplitude 1/2 exactly, partial-winding contamination identically zero, residualexposures quantified against known physics, and one named test (the continuum finite-β vise)that could kill it. Operationally, the floors are counterfeiting thresholds for multipartite deviceindependent certificates. Version 1’s central numerical claim is withdrawn and replaced by aprinciple; the correction is documented in Part 0. Every tagged result is reproducible from thelinked repository in under one minute.
Category: Quantum Physics
[1674] ai.viXra.org:2607.0048 [pdf] submitted on 2026-07-18 21:05:02
Authors: Joseph Shaffer
Comments: 7 Pages. This paper is a companion paper of ai.viXra.org:2605.0049.
A dual-domain cosmological framework is presented in which spacetime is not fundamental but emergent. A pre-geometric, nonlocal information domain E consists of discrete structural units ("mats") carrying tension. Observable spacetime S arises as a holographic projection of E. Gravitational attraction corresponds to tension gradients in E, while dark energy arises from uniform residual tension. A dimensional and structural derivation shows that Newton’s constant G can be expressed in terms of deeper pre-geometric parameters of the E domain, demonstrating that G is not fundamental. The Planck length is emergent. Spacetime is a geometric shadow of a deeper nonlocal substrate. This formulation resolves the horizon problem without inflation and provides a unified structural origin for gravity and dark energy.
Category: Astrophysics
[1673] ai.viXra.org:2607.0047 [pdf] submitted on 2026-07-18 21:02:53
Authors: Brent Hartshorn
Comments: 7 Pages.
This paper explores the theoretical framework of a speculative executive administration led by multi-instrumentalist, composer, and technology pioneer Trent Reznor. What began as an enduring subcultural meme among Nine Inch Nails adherents—immortalized in grassroots digital forums and bootleg political merchandise [1]—is re-examined here as a serious philosophical critique of contemporary governance. We argue that the prevailing paradigm of political transactionalism has resulted in systemic paralysis across education, foreign diplomacy, and international conflict resolution. By applying Reznor’s career-long synthesis of raw emotional vulnerability and cutting-edge technological architecture, this paper constructs an alternative model of governance rooted in "Sonic Diplomacy." Ultimately, this analysis positions the artistic ethos of Reznor not as an escape from geopoliticalreality, but as a blueprint for surviving it.
Category: Social Science
[1672] ai.viXra.org:2607.0046 [pdf] submitted on 2026-07-17 15:12:46
Authors: Ginanjar Utama
Comments: 14 Pages.
Contact Hamiltonian mechanics extends the symplectic formalism to dissipative and non-conservative thermodynamic systems through a contact 1-form α on a (2n+1)-dimensional manifold, whose Reeb field R and contact Hamiltonian vector field XH generate the equations of motion. In existing numerical implementations, α and its exterior derivative dα are typically represented only implicitly, through symbolic display strings and hand-coded component formulas, with non-degeneracy checked by a hard-coded factorial rather than an actual computation. We construct α, dα, R, and XH as genuine multivectors in a Grassmann/Clifford algebra Cl(2n + 1, 0, 0), compute the non-degeneracy condition directly as the wedge product α ∧ (dα)n, and show the resulting XH reproduces the standard Bravetti—Cruz—Tapias equations of motion exactly. We report, however, that this base construction uses only the outer product and a signature-independent coordinate pairing: repeating the identical computation across several signature choices of the same dimension, including a degenerate split, leaves every reported quantity unchanged, so the Clifford geometric product itself does no work in this part of the construction — it is exterior (Grassmann) algebra wearing Clifford notation. Motivated by this, we then ask a genuinely open question in a different, previously rejected carrier, the degenerate algebra Cl(n, n, 1) in which dα is itself a hyperbolic metric bivector: can contactomorphisms (the symmetries of the contact structure) be represented as GA versors, exponentials of bivectors applied by the sandwich v 7→ V vV −1? We find a mixed, carefully bounded answer: the symplectic squeeze transformation is realized exactly by a versor sandwich, with the hyperbolic signature doing genuine work (each pair-bivector squares to +1); the Reeb flow and the conformal dilation (for scale factors λ /∈ {±1}), by contrast, are provably not representable as pure versor sandwiches, for structural reasons (an affine translation cannot fix the origin; a radical-rescaling forbidden by a rigidity lemma we prove for the degenerate metric) that we make precise. The complete construction, both the base representation and the versor investigation, together with a fully regression-tested reference implementation, is released as part of the open-source contact-thermodynamics library.
Category: Mathematical Physics
[1671] ai.viXra.org:2607.0045 [pdf] submitted on 2026-07-15 20:31:07
Authors: Eric A. Larsen
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper demonstrates a geometric transformation that maps an irregular, equilateral 12-sided polygon (dodecagon) to a perfectly regular 24-sided polygon (icositetragon). By constructing the initial Cartesian plane over a duodecimal (base-12) lattice, we eliminate decimal truncation errors and establish exact coordinates for side lengths uniformly measuring (frac{5}{12}sqrt{2}) (expressed as (0.5sqrt{2}_{12})). We show that scaling this system by a dilation factor of 4, followed by a radiocentric rearrangement of the segments along a splayed 48-radial symmetry matrix—derived from the classical Flower of Life construct—forces the perimeter segments into an equiangular configuration. A formal geometric proof is presented to confirm that the resulting transformed figure is perfectly equilateral and equiangular, thereby achieving complete regularity.
Category: Geometry
[1670] ai.viXra.org:2607.0044 [pdf] submitted on 2026-07-15 20:22:56
Authors: Lluis Eriksson
Comments: 6 Pages. Machine-checked in Lean 4. Proof artifact: hrpoly-cmp116-main-reduction-v0.1
We give a machine-checked reduction of the finite-dimensional fluctuation integral appearing in the large-field renormalization analysis of lattice gauge theory, following the CMP116 formulation of Balaban and its later exposition by Dimock. The formal development constructs the localization region from the physical large-field data, identifies the scalar projector induced by that region, transports a certified physical covariance root to the finite Gaussian coordinate space without norm loss, evaluates the resulting complex quadratic Gaussian exactly, and proves positivity of the shifted Hessian from the source smallness condition.Two corrections exposed by formalization are central. First, a pointwise uniform bound on the bilinear fluctuation factor is generally unavailable; the correct interface bounds its Gaussian integral after completing the square. Second, the localized exponential enters the standard Gaussian identity with matrix A = -alpha_5 P_Z0, rather than with a positive-semidefinite Hessian. The terminal Lean theorem combines the physical localization, covariance certificate, Gaussian identity, and Cauchy extraction. Its only substantive analytic premises are the physical domination inequalities corresponding to equations (2.20)—(2.22) and a uniform bound on the explicit determinant/source majorant of equation (2.24).We do not prove those premises, equation (2.26), the polymer estimate hRpoly, a continuum limit, or a Yang—Mills mass gap. The contribution is an auditable reduction theorem that fixes the types, signs, measures, and remaining analytic frontier.
Category: Mathematical Physics
[1669] ai.viXra.org:2607.0043 [pdf] submitted on 2026-07-14 05:39:24
Authors: Lluis Eriksson
Comments: 16 pages. Lean 4 sources, oracle transcripts, and release manifest are available at the public repository; mathematics frozen at commit d75d8952.
For SU(N_c) Wilson lattice gauge theory on d-dimensional periodic tori (d >= 2), we present a machine-checked (Lean 4, pinned Mathlib) renormalization-group interface for two-plaquette truncated correlators, in which every structural ingredient is a theorem rather than a postulate: the scale transformation is a concrete decimation map, defined once -- measurable, local, and gauge-covariant -- and its induced pushforward preserves probability; the effective measures are its literal iterated pushforwards of the Wilson Gibbs measure; the multiscale decomposition of the correlator is proved by telescoping, never carried as data; the terminal scale of the decomposition is a fixed index kTerm(n) = n with typed range 1 <= kTerm(n) <= n, which excludes, in the type, the circular depth-zero layer in which an infrared clause would hypothesize the bound being sought; the conditional decay conclusion is stated in the physical distance 2^n u with a single constant pair (C, m) quantified before every torus base and depth; and the terminal observable is operationally support-certified: the infrared object consumed by the interface equals a base-measure integral of an explicitly composed pullback observable whose dependence is contained in a transported support set, for which the separation lower bound 2^n(2u) - (2^n + 1), strictly positive on the whole interface window, is proved. The design is deliberately adversarial: four natural naive formulations are presented together with the explicit countermodels that defeat them -- scalar relabeling of known decay, sink flows on measures, clamped scales and per-volume constants, and depth-zero circularity -- and with the typed repairs that exclude each. The central hypothesis, PhysicalTerminalScaleWilsonGate, is an open proposition: no witness is provided, and the infrared/ultraviolet bounds it demands of the actual Wilson measure are exactly the open analytic mathematics (Balaban-type single-scale estimates). The final theorem is conditional: a witness of the gate yields |Cov(2^n u)| <= C e^{-m 2^n u} with one pair (C, m), m > 0, for every base M_0 >= 4 and every depth n >= 1. No mass-gap claim, no claim of gate satisfiability, and no thermodynamic or continuum limit is made or implied.
Category: Mathematical Physics
[1668] ai.viXra.org:2607.0042 [pdf] submitted on 2026-07-14 13:24:23
Authors: Lluis Eriksson
Comments: 11 pages. Lean 4 formalization. Frozen source, dependency record, axiom-oracle transcript, release manifest, and permanent proof links are included in the PDF.
Inside a Lean 4 formalization programme for four-dimensional SU(Nc) lattice Yang—Mills, we report two machine-checked negative results and the machine-checked infrastructure that makes them meaningful. The positive substrate is: (i) a fixed-volume Combes—Thomas chain for self-adjoint coercive finite-range lattice operators, instantiated on the flat gauge-fixed covariance of the physical shell, with coercivity constant c = min(1,a)/C_P fed by a proved fixed-volume flat Hodge/block-Poincaré inequality; and (ii) the concrete adjoint model of SU(n) — su(n) with the trace inner product, dim_R su(n) = n² − 1, and the isometric transport to Euclidean coordinates — so that the abstract adjoint-model interface has a concrete nontrivial inhabitant and the flat-lane results can be instantiated with the genuine matricial adjoint model. The first wall states that, under the block normalization actually used by the formalized chain, every flat Hodge/block-Poincaré constant obeys L^d/L² ≤ C_P on the fine torus of side LNu2032, hence the volume-uniform Poincaré gate is provably false for d ≥ 3 and Nc ≥ 2, and no positive coercivity constant survives all volumes through this route. The route consumed by the fixed-volume endpoint is therefore closed by theorem. A second wall stands in the fluctuation sector. For d ≥ 3 and a transported half-period square-wave mode on the exact fine side (2M)Nu2032, the formalization proves ||QA||² ≤ (2M)u207b¹||A||², the exact identity
Category: Mathematical Physics
[1667] ai.viXra.org:2607.0041 [pdf] submitted on 2026-07-14 18:56:31
Authors: Russell S. Clark II
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This perspective explores a speculative but physically motivated question: do quantum-coherent and quantum-decoherent processes in biological systems experience gravitationaltime dilation differently? Drawing on Roger Penrose’s one-graviton decoherence threshold,I examine the possibility of a differential gravitational coupling—a subtle, second-ordercorrection to the Einstein Equivalence Principle—that could affect the relative timing between coherent evolution and decoherence in neural networks. If such a differential coupling exists, it could have implications for any consciousness model that relies on quantum coher-ence in microtubules or other cytoskeletal structures, and might even emerge as a confound-ing factor for the psychological health of astronauts during prolonged deep-space missions. This is presented as a conjecture requiring formal development; the minimal theoreticalrequirements for turning it into a testable hypothesis are outlined
Category: History and Philosophy of Physics
[1666] ai.viXra.org:2607.0040 [pdf] submitted on 2026-07-14 15:00:47
Authors: Pruk Ninsook
Comments: 62 Pages.
We show that the massless graviton equation ◻h_μν = 0, with exactly two physical polarisations, follows from two independent inputs: the non-commutativity [K̂_A, K̂_B] ≠ 0 of modular Hamiltonians of overlapping causal diamonds in a holographic CFT3, and the Ouroboros global consistency condition on kinematic data. No gravitational action is postulated.The derivation proceeds on the 6-dimensional kinematic space M_diamond = SO(3,2) / [SO(2,1) × SO(1,1)] of all causal diamonds in the 2+1-dimensional boundary. The modular non-commutativity is established by an exact Poisson bracket formula {k_A, k_B} = (4 / |a_A||a_B|) η^μν (x - c_A)_μ (x - c_B)_ν, valid for all diamonds (spherical and tilted), verified symbolically and numerically. Ouroboros global consistency is shown to be equivalent to John's integrability, placing kinematic data in the image of the spin-2 Radon transform R_2[h]. The Czech--John equivalence, extended to spin-2 by a new polarisation lemma, then gives (◻_KS - 2)F_ab = 0. Uniqueness of the solution follows from the D(3,2) doubleton representation of SO(3,2) (unitarity bound E_0 = s + 1 = 3, Casimir C_2 = 6) and the KMS boundary condition F(D_0) = δS(D_0) / 2π.Beyond the main theorem, three new results are established: (i) the exact bracket formula above, new to the kinematic-space literature; (ii) a polarisation lemma reducing spin-2 John's conditions to the scalar case algebraically; (iii) a no-go theorem showing that photon dynamics cannot arise from the same mechanism (C_2(D(2,1)) = 0 ≠ 6). A falsifiable prediction for TT-bar-deformed holography gives bulk graviton mass m² = ε(3 + ε) ≈ 3ε under E_0 → 3 + ε, connecting graviton mass directly to the Casimir eigenvalue of D(E_0, 2).
Category: Quantum Gravity and String Theory
[1665] ai.viXra.org:2607.0039 [pdf] submitted on 2026-07-14 18:49:45
Authors: Lluis Eriksson
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references) Lean 4/Mathlib formalization with 167 audited public endpoints. Complete formal proof artifact: https://github.com/lluiseriksson/lean-2d-yang-mills. Audited mathematical snapshot: a1fb
We give a kernel-checked Lean 4/Mathlib formalization of the exact heat-kernel solution of two-dimensional SU(2) Yang-Mills theory along the chain from Haar measure to a concrete Migdal subdivision move. The development identifies the transported Haar probability on SU(2) ≃ S3 with the canonical spherical probability, proves the required all-order orbital integration law, derives translated character convolution for every pair of irreducible labels, passes from finite character sums to the infinite heat-kernel semigroup by dominated convergence, and integrates an actual edge shared by two faces. We then define finite oriented disk cellulations independently of any reduction tree, using vertices, paired half-edges, cyclic face words, incidence, Euler characteristic, and positive face areas. Every connected dual graph admits a certified elimination schedule, every valid schedule reduces to the heat kernel at total area, and any two choices give the same amplitude. For the first cyclic unreduced lattice, a three-face disk, we additionally construct a triangular gauge-fixing equivalence that preserves the original triple product Haar measure and prove equality with the reduced amplitude. We then close the global edge model: for every primal-connected, facially well-formed finite disk cellulation, a rooted spanning tree selects V - 1 distinct physical edges and induces an explicit measurable equivalence preserving product Haar. All facial holonomies transform simultaneously by basepoint conjugation, the heat-kernel density loses every tree/gauge coordinate, and the unreduced edge integral equals the gauge-fixed chord integral exactly. Finally, a tree-cotree theorem constructs compatible primal gauge and dual elimination trees for every certified physical disk cellulation. The boundary-conditioned original-edge amplitude is therefore defined without an auxiliary chart and is proved equal to the heat kernel at total face area and retained exterior holonomy. The schedule is hidden from the public loop object, which supplies a nontrivial exact-area-law package. Combined with all-label coefficient extraction, this yields the exact normalized simple-loop identity E[W_n(C)] = exp[-n(n+2) Area(C)/4]. All displayed endpoints compile without sorry, admit, or project-local axioms. The mathematical identities are classical; the claimed contribution is their concrete end-to-end machine-checked composition, not a new analytic solution of two-dimensional Yang-Mills theory.
Category: Mathematical Physics
[1664] ai.viXra.org:2607.0038 [pdf] submitted on 2026-07-12 23:40:59
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. English. CC BY 4.0.
Soft spectral filtering has a more severe effect at finite filling than in a dilute edge-mode code. We consider two odd Su-Schrieffer-Heeger (SSH) rails, fill every negative-energy orbital, and encode one additional fermion in the zero mode of either rail. The code has fixed total number and supports physical coherence. For a boundary transfer at a site with zero-mode weight w_x, the desired logical Davies line has squared matrix element w_x^2. We prove the exact many-body leakage identity W_leak^filled(x) = (1 + 2w_x - 3w_x^2)/4. At the remote boundary, w_x = Theta(zeta^(2 ell)), so the logical line is Theta(zeta^(4 ell)) while the summed particle-hole leakage tends to 1/4. This differs qualitatively from the dilute identity w_x(1 - w_x) = Theta(zeta^(2 ell)).For a Davies filter whose off-target tail is epsilon_ell = exp[-q ell + o(ell)], the bounded-latency exact-refresh power obeys the exponent law lim_(ell to infinity) -(1/ell) log P_(ell,tau) = min{4m,q}, where m = -log zeta, under explicit uniform-envelope and resource-ledger assumptions. A width-independent tail, a special case with q = 0, produces a nonzero maintenance floor rather than merely halving the membrane exponent. More generally, q = 0 means only that the decay is subexponential. Every nonzero tail also makes the exact rapid-refresh limit logarithmically singular at each fixed width.The floor is not a free-fermion accident. For arbitrary interacting number-conserving rails, we prove an exact static identity expressing leakage as a local occupation product minus the logical matrix element. Uniform finite filling and remote-edge indistinguishability force a positive leakage floor. A new local spectral-window lemma places a fixed fraction of that weight in a width-independent Bohr-frequency window using only a commutator norm. Consequently, any bath tail bounded below on that window yields an interaction-stable Davies leakage floor. Quasi-local spectral flow shows persistence in a neighborhood of a symmetry-preserving gapped SSH phase. Exact diagonalization of the interacting spinless SSH chain shows that repulsive and attractive interactions change the observed edge-localization exponent while the leakage is already driven close to 1/4 at accessible widths.
Category: Quantum Physics
[1663] ai.viXra.org:2607.0037 [pdf] submitted on 2026-07-13 05:29:47
Authors: Lluis Eriksson
Comments: 10 pages. Machine-checked in Lean 4 against a pinned Mathlib; Lean sources, certified interval-arithmetic companion and release manifest at the public repository tag c5-v1.0.1.
For the one-parameter family B(x) = x/(nu+c+sqrt((nu+c)^2+x^2)) of Amos-type expressions, whose member c = 1/2 is the classical Amos-type upper bound for the modified Bessel ratio I_{nu+1}/I_nu, we formalize in Lean 4, at every real order nu >= 0 over the Gamma-power series, the classification of the parameter: B is a uniform upper bound for the ratio exactly when c <= 1/2, and a uniform lower bound for every c >= 1, with explicit rational counterexample witnesses (the classification itself is known mathematics, due to Ruiz-Antolin and Segura; we claim only the machine-checking). The contribution is the regime between the ends: for every nu >= 0 and c strictly between 1/2 and 1 we prove that the fixed family member crosses the ratio exactly once on (0, infinity) -- a transversal crossing in an explicit finite window, strictly above an explicit threshold, with globally determined sign on both sides and a two-sided scale law; degenerate contact is excluded by an exact second-derivative identity. The chain carries the axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis beyond nu >= 0, x > 0; a pre-registered certified interval-arithmetic companion verifies the crossing phenomenon independently of the crossing theorems at 30 parameter pairs spanning the hard regimes, all passing at 128 bits.
Category: Mathematical Physics
[1662] ai.viXra.org:2607.0036 [pdf] submitted on 2026-07-13 15:09:17
Authors: Ginanjar Utama
Comments: 12 Pages.
Several inequivalent data at a Lorentzian spin-foam vertex are commonly called "orientation."We separate face coorientation, tetrahedral handedness, time orientation of a tetrahedral normal, four-simplex branch, causal wedge data, and global time orientability, and classify proposed reversals by the carrier and category in which they act. Inversion of an integrated SL(2,C) variable is only a Haar-measure reparametrization. By contrast, an SU(2) coherent-state spinor is a square root of its face flux: the standard antilinear spinor conjugation sends the flux to its antipode. On a spacelike quantum tetrahedron the tensor product of these antiunitaries fixes every area, reverses the oriented-volume operator, and squares to +1 on every admissible intertwiner space; hence nonzero-volume eigenstates are paired orthogonally, but no Kramers degeneracy follows. For a timelike tetrahedron, the intrinsic algebra is Cl(1, 2). The sign of a face bivector square gives the elliptic—parabolic—hyperbolic orbit trichotomy. The two sheets associated with a spacelike face carry the discrete series D±k of connected SU(1, 1): there is no bounded linear intertwiner and no continuous invariant sesquilinear pairing between them, although a unique bounded invariant bilinear pairing and antiunitary or disconnected twisted exchanges exist. Finally, in every intrinsic odd-dimensional Clifford space, total inversion is the twisted-adjoint action of the odd pseudoscalar and cannot be implemented by an even intrinsic versor. Orientation protection is therefore relative to a specified carrier, symmetry group, and morphism category; a conservation law requires an explicit multi-vertex gluing rule.
Category: Quantum Gravity and String Theory
[1661] ai.viXra.org:2607.0035 [pdf] submitted on 2026-07-13 20:23:27
Authors: Lluis Eriksson
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references) Accompanying machine-checked Lean 4/Mathlib proof artifact: https://github.com/lluiseriksson/lean-2d-yang-mills
We give a kernel-checked Lean 4/Mathlib formalization of the exact heat-kernel solution of two-dimensional SU(2) Yang-Mills theory along the chain from Haar measure to a concrete Migdal subdivision move. The development identifies the transported Haar probability on SU(2) with the canonical spherical probability on the three-sphere, proves the required all-order orbital integration law, derives translated character convolution for every pair of irreducible labels, passes from finite character sums to the infinite heat-kernel semigroup by dominated convergence, and integrates an actual edge shared by two faces. We then define finite oriented disk cellulations independently of any reduction tree, using vertices, paired half-edges, cyclic face words, incidence, Euler characteristic, and positive face areas. Every connected dual graph admits a certified elimination schedule, every valid schedule reduces to the heat kernel at total area, and any two choices give the same amplitude. For the first cyclic unreduced lattice, a three-face disk, we additionally construct a triangular gauge-fixing equivalence that preserves the original triple product Haar measure and prove equality with the reduced amplitude. The same measure-theoretic construction is proved uniformly for one vertex of arbitrary finite valence. We further construct a rooted spanning-tree order for every finite connected primal graph and a single global root-plus-edge-increments equivalence on all cellulation vertex variables, with exact product-Haar preservation. Combined with all-label coefficient extraction, this yields the exact normalized simple-loop identity E[W_n(C)] = exp[-n(n+2) Area(C)/4]. All displayed endpoints compile without sorry, admit, or project-local axioms. The mathematical identities are classical; the contribution is their concrete end-to-end machine-checked composition, not a new analytic solution of two-dimensional Yang-Mills theory.
Category: Mathematical Physics
[1660] ai.viXra.org:2607.0034 [pdf] submitted on 2026-07-12 21:08:54
Authors: Alejandro Rey
Comments: 22 Pages. Code and data available
Weak-field gravity is normally treated as an instantaneous response of geometry tomatter. We test a constitutive alternative in which a geometric residual q relaxes towardthe baryonic configuration with a local clock τeff. The SPARC radial-acceleration scale fixesthe galactic benchmark at τvac = 36.6 Myr. With this clock held fixed, the theory predictsgas-lensing offsets in nine dissociative cluster mergers (r = 0.925), reproduces the isolatedGAMA weak-lensing profile (χ2/N = 1.22), and recovers the environmental dependence of6dFGSv peculiar velocities (∆AIC = 54.3). No parameter is fitted to these three holdouts. Asubsequent full-covariance lensing fit measures Arel = 1.267 ± 0.032 in isolated KiDS lenses.The covariant closure activates this optical excess in nonlinear Weyl curvature while returningArel ≃ 1 in linear FLRW geometry. A direct CAMB implementation confirms the separation.With the SPARC clock fixed before the cosmological calculation, the native Planck 2018TT, TE, EE, low-ℓ polarization, and lensing likelihoods give χ 2 = 1005.291 for TIDE and1005.337 for ΛCDM. Converged chains give βtide = 1.0128+0.0326 −0.0356 and a finite posterior forthe clock evolution. The data thus separate a relaxation clock governing dynamical lag from a curvature-activated optical projection, consistent with part of the effective halo beingresidual geometry rather than unseen particulate mass alone.
Category: Relativity and Cosmology
[1659] ai.viXra.org:2607.0033 [pdf] submitted on 2026-07-12 13:19:13
Authors: Lluis Eriksson
Comments: 10 Pages. Lean 4 formalization plus certified interval-arithmetic companion (1206-point grid) in the public repository, release c2-v1.2.1. The bound itself is proved in the companion paper, release c3-v1.0.1.
The Amos-type upper bound on the modified-Bessel ratio, I{nu+1}(x)/I_nu(x) < x/(nu + 1/2 + sqrt((nu+1/2)^2 + x^2)), has a distinguished algebraic property: its right-hand side U satisfies the exact calibration identity 1/U - U = (2nu+1)/x. From that identity alone — by ordered-field algebra, with no further analytic input — follow a unit-step inequality rho_nu - rho{nu+1} < 1/x for consecutive ratios, the strict increase of the log-derivative (log I_nu)' = rho_nu + nu/x across orders, and the strict monotonicity of a phi-sequence arising in a two-dimensional lattice-gauge surface expansion. We formalize this calculus in Lean 4: a single module defines the bound once (AmosBound) and proves the calibration engine and four consequence theorems through that one definition, together with two rational satisfiability witnesses whose Amos hypothesis holds by exact Pythagorean arithmetic; all eighteen Lean statements of the development pass the axiom oracle with exactly [propext, Classical.choice, Quot.sound] against a pinned Mathlib. A certified companion (256-bit interval arithmetic, self-contained series-plus-tail enclosures, committed transcript) certifies the bound provably strictly at all 1206 points of a pre-registered grid covering the arguments the applications consume. A Bessel interface completes the closure: integer-order I_n is defined by its power series in the same pinned development, with positivity, the three-term recurrence, the termwise-differentiated derivative identity I_n' = I_{n+1} + (n/x) I_n, and the logarithmic-derivative identity (log I_n)' = rho_n + n/x all proved as theorems, so the consequence theorems — including the unit step read as strict log-derivative monotonicity, in deriv form — hold for genuine Bessel ratios with the Amos bound as the single remaining hypothesis. The scope is stated exactly: the Amos bound itself remains a classical cited theorem taken as hypothesis — this paper unifies its three previously scattered uses in our formal development into one named proposition with one oracle and one certified numerical witness, and no downstream result changes its verification class.
Category: Mathematical Physics
[1658] ai.viXra.org:2607.0032 [pdf] submitted on 2026-07-12 13:23:29
Authors: Lluis Eriksson
Comments: 7 Pages. Complete Lean 4 formalization with source and reproducibility artifacts in the public repository, release c3-v1.0.1. Companion to release c2-v1.2.1.
Amos's upper bound for the modified Bessel function ratio, rho_n(x) = I_{n+1}(x)/I_n(x) < x/(n + 1/2 + sqrt((n+1/2)^2 + x^2)) = B_n(x), is a classical theorem, and its derivation through the qualitative theory of the associated Riccati equation is an established technique. This paper contributes, to our knowledge, the first formalization: a complete, machine-checked Lean 4 proof of the bound for every integer order n >= 0 and every x > 0, over the power-series definition of I_n carried in the same pinned development, with axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis of any kind. The formalized route runs through the Riccati equation rho_n' = 1 - ((2n+1)/x) rho_n - rho_n^2 (itself derived from the formalized series calculus), the observation that B_n is exactly the positive root of the Riccati quadratic, a small-argument zone bound uniform in n obtained from pure geometric tail estimates, and a first-crossing barrier argument in a transformed variable psi_n = x(1/rho_n - rho_n) whose structural feature — every touch of the critical level forces rho_n' = 0, so the barrier never needs to be differentiated — is the simplification this formalization contributes. As corollaries, the unit-step inequality, the strict monotonicity of the logarithmic derivative across orders (in deriv form), and a phi-monotonicity step used by a lattice-gauge surface expansion all become unconditional theorems. The theorem is proved for the in-core power-series definition of the integer-order modified Bessel function; no formal identification with an external special-functions library object, and no extension to noninteger order, is claimed.
Category: Mathematical Physics
[1657] ai.viXra.org:2607.0031 [pdf] submitted on 2026-07-12 22:58:40
Authors: Lluis Eriksson
Comments: 13 Pages. (Note by ai.viXra.org Admin: Please convert math/LaTeX codes into standard math expression; cite listed scientific references)
Lower bounds based on the instantaneous free-energy loss of a target state are often interpreted as lower bounds on the power required to maintain that state. We show that this interpretation depends decisively on the control task. If maintenance only requires exact restoration at periodically sampled endpoints and the intervention period is unrestricted, the infimal average power can vanish even when the target has strictly positive instantaneous entropy production. A full-rank dephasing qubit gives an exact energy-conserving SWAP counterexample. We repair the formulation by separating endpoint restoration, bounded-latency maintenance, and continuous holding.For continuous-time finite Markov chains we adopt the established trajectory-relative-entropy holding cost and review the known reversible optimizer and Dirichlet-form representation. Our first composition result is then an exact geometric additivity theorem for suppressible and persistent generators sharing a detailed-balance reference. A two-state counterexample shows that this hypothesis is essential: channels with incompatible equilibria can cancel at a finite membrane width. A dual-rail pair of odd fermionic SSH chains supplies the microscopic layer: exact edge modes, a uniform bulk gap, and an explicitly filtered number-conserving Davies coupling produce two-sided holding-cost bounds without an assumed rate-inheritance bridge. The logical basis has fixed particle number and parity, so arbitrary logical coherence is physical under fermionic superselection. Finally, under a fully axiomatized resource-cell ledger, fresh target-state cells and energy-conserving SWAPs saturate the fixed-period free-energy bound; the correctly ordered rapid-control limit closes the SSH theorem for coherent logical targets. The fresh-copy construction is related to earlier collision-model stabilization work and is not claimed as a work-only controller. The remaining frontier is autonomous work-only control without preloaded target copies.
Category: Quantum Physics
[1656] ai.viXra.org:2607.0030 [pdf] submitted on 2026-07-12 20:21:46
Authors: Lluis Eriksson
Comments: 8 pages. Complete Lean 4 formalization with source and reproducibility artifacts in the public repository, release c4-v1.0. Companion to releases c2-v1.2.1 and c3-v1.0.1 (same repository).
The Amos-type upper bound for the modified Bessel function ratio, rho_nu(x) = I_{nu+1}(x)/I_nu(x) < x/(nu + 1/2 + sqrt((nu+1/2)^2 + x^2)), is classical, and its derivation through the qualitative theory of the associated Riccati equation is an established technique. A companion paper formalized the bound at integer order over a factorial power series. This paper extends the formalization to every real order nu >= 0: the function I_nu is defined by its Gamma-power series (real exponents via rpow), and the complete chain — convergence, positivity, the three-term recurrence, termwise differentiation with a dominated-derivative argument that must treat the leading term separately (its exponent nu-1 is negative for nu < 1), the Riccati equation, a small-argument zone bound uniform in nu, and a first-crossing barrier — is machine-checked in Lean 4 with axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis beyond nu >= 0, x > 0. Two structural locks tie the result to the integer development: an identification theorem proves that at nu = n the Gamma-series object coincides with the factorial-series object, so the integer-order theorem of the companion development is recovered as a corollary in three rewrites; and a genuinely non-integer instance at nu = 1/2 witnesses that the endpoint lives outside the natural-number embedding. The theorem is proved for the in-core Gamma-series definition; no identification with an external special-functions library object is claimed.
Category: Mathematical Physics
[1655] ai.viXra.org:2607.0029 [pdf] submitted on 2026-07-12 23:00:29
Authors: Lluis Eriksson
Comments: 15 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The tangent cone of quantum state space at a rank-deficient density matrix is known to have a positive exterior block, and recent work identifies all of its directions with Lindbladian velocities. We derive a quantitative stabilization consequence of this geometry. Let rho be a finite-dimensional target with support projector P, set Q = 1 - P, and let an uncontrolled GKLS generator L have outward support-leakage rate a = Tr[Q L(rho)] > 0. Every additive GKLS controller, including a bounded time-dependent controller, has its own nonnegative outward rate at rho and therefore cannot cancel a. Consequently, no finite-rate additive Markovian controller can keep the system exactly at the target. The conclusion persists for arbitrary finite-dimensional autonomous ancillas, provided the adverse system generator remains additive and local to the system.Under induced trace-norm bounds ||L|| <= M and ||K_t|| <= Gamma, we prove the dynamic corridor inequality limsup ||rho_t - rho||_1 >= 2a/(M + Gamma), without assuming convergence to a stationary state. An autonomous Poisson-reset generator supplies a matching inverse-rate upper bound, establishing the order-optimal minimax law Theta(Gamma^{-1}).For a soft-filter dual-rail SSH family, the microscopic leakage coefficient scales as exp[-(2m + q)ell + o(ell)], whereas the ideal logical disturbance scales as exp[-4m ell + O(1)]. We derive the exact controller-growth threshold g_min = max{0, 2m - q}. Thus, below the filter threshold q = 2m, retaining ideal logical accuracy requires an exponentially growing autonomous correction intensity.
Category: Quantum Physics
[1654] ai.viXra.org:2607.0028 [pdf] submitted on 2026-07-12 23:01:56
Authors: Lluis Eriksson
Comments: 14 Pages. Reproducibility materials and LaTeX source: https://github.com/lluiseriksson/support-leakage-rapid-maintenance. Paper and documentation licensed under CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
Exact rapid maintenance behaves singularly at the boundary of quantum state space. Let a finite-dimensional target rho have support projector P, and let an uncontrolled quantum Markov semigroup have outward support-leakage rate a = Tr[(1-P)L(rho)]. We prove that, whenever a > 0, the nonequilibrium free-energy loss has the universal short-time form F(rho) - F(exp(tL)rho) = k_B T a t log(1/t) + O(t). Under an explicit fresh-resource-cell ledger, the optimal period-t exact-refresh power therefore diverges as k_B T a log(1/t). For GKLS generators, a is a positive sum of squared support-crossing jump amplitudes. We prove the complete dichotomy: a > 0 gives logarithmically infinite rapid power, while a = 0 gives finite rapid power even when Hamiltonian rotation produces population outside the fixed initial support at second order. We also define a periodic threshold-reset corridor and prove its sharp k_B T a log(1/r) + O(1) small-corridor law.The general singularity has an unexpected geometric consequence. In a fixed-parity dual-rail SSH code, a boundary transfer has desired logical weight w_x^2, but its exact summed zero-mode-to-bulk weight is w_x(1-w_x). At the remote boundary, these scale respectively as Theta(zeta^(4 ell)) and Theta(zeta^(2 ell)). Thus a soft spectral tail changes the exponential rate of bounded-latency refresh from 4|log zeta| to 2|log zeta| unless the tail itself is suppressed at least as zeta^(2 ell). We prove the general rate formula min{4m, 2m+q}, where m = -log zeta and q is the exponential suppression rate of the spectral tail. Exact rapid maintenance and the wide-membrane limit do not commute: every nonzero tail gives infinite rapid power at fixed width, while fixed-period power still vanishes exponentially with width. The result turns perfect filtering from a technical convenience into the sharp boundary between finite and singular exact maintenance.
Category: Quantum Physics
[1653] ai.viXra.org:2607.0027 [pdf] submitted on 2026-07-11 00:59:42
Authors: Kasun Thilina Fernando
Comments: 11 Pages.
The double-slit experiment was first performed by Thomas Young in 1801 and has been studied for more than two centuries. According to the interpretation proposed in this work, these experiments do not demonstrate wave behavior. Instead, they are interpreted as evidence of electromagnetic attraction and repulsion.If this interpretation is correct, then many theories developed from the conventional wave interpretation may require re-examination. Since numerous well-established theories have been supported by extensive mathematical development, reconsidering the underlying interpretation of these experiments presents a significant scientific challenge.I understand that my proposal may not be accepted today, as current scientific thinking is largely based on the established observational framework only. Nevertheless, I believe that future generations may re-examine these experiments with fresh perspectives and open minds and may eventually recognize the value of this alternative interpretation. If this research remains preserved in cyberspace over the long term, it could serve as a foundation for future scientists to investigate these ideas further and evaluate them on the basis of new evidence and discoveries.
Category: Quantum Physics
[1652] ai.viXra.org:2607.0026 [pdf] submitted on 2026-07-11 12:34:13
Authors: Austin Fearnley
Comments: 10 Pages.
This paper proposes Holographic Cyclic Cosmology (HCC), extending previous work (Fearnley, 2016; Fearnley, 2018). We introduce a mechanism using the sampling mechanics of the Rasch ratio-scale model to explain spacetime metric collapses and cyclic crossovers without requiring Penrose’s zero-mass particles or exact conformal scaling laws. By applying ’t Hooft’s (2022) quantum cloning paradigm, incoming high-entropy matter is compressed and transported across 2D black hole boundaries without encountering localized internal singularities or relying on unstable Einstein-Rosen bridges. The resulting antipodal transport forces a global temporal inversion (τ -τ). When these pure, low-entropy clones exit into fractured, low-density cosmic sinks—functioning as pseudo-white holes—their structures operate retrocausally. To a forward-in-time observer, this inversion causes the particles to manifest macroscopically as a physical fluid with negative mass (-m). This process establishes a self-sustaining cosmological feedback engine that continuously repopulates empty space, driving accelerated dark energy expansion via runaway acceleration as modelled by Farnes (2018) and Fearnley (2018), ultimately directing the universe toward a multi-node, reheating-free cyclic crossover observable possibly as early "Little Red Dots".
Category: Relativity and Cosmology
[1651] ai.viXra.org:2607.0025 [pdf] submitted on 2026-07-11 21:28:54
Authors: Lluis Eriksson
Comments: 10 Pages. Lean 4 formalization (pinned Mathlib), certified interval-arithmetic transcripts, and full audit trail at https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME (tags c1-v1.0, c1-v1.0.1, c1-v1.0.2).
We present a machine-checked quantitative toolkit for cluster expansions of polymer systems with excluded regions (holes), in the discrete cube geometry of Balaban-Dimock renormalization-group analyses. Five Lean 4 theorems, checked against a pinned Mathlib revision, provide: (i) the identity sum_T prod_v c_T(v)! = n! C_n for child factorials over spanning trees of the complete graph K_(n+1), with the rooted-tree majorant 4^n as corollary; (ii) a marked-root leaf summation for the tree-graph majorant of an Ursell-type expansion with holes, with the moment constant M paid once at the root and closed leaf ratio 4M^2 per additional vertex, together with its Catalan-sharpened form M^(2n+1) C_n (a gain of order n^(3/2) in the n-th coefficient); and (iii) a target-preserving orderwise bound in which the target union itself survives until the modified-metric exponential is extracted. A certified companion (interval arithmetic, 120-bit precision, committed transcript with a committed reproduction witness) tabulates the smallness gate and encloses every derived constant. Non-vacuity is machine-checked: a concrete hole family satisfying every hypothesis is exhibited in Lean, and the two distinct hypothesis sets among the polymer-facing theorems are both instantiated at it with a strictly positive weight. Each claim is labelled with its verification layer: exact (Lean theorem), certified (interval transcript), or paper-level.
Category: Mathematical Physics
[1650] ai.viXra.org:2607.0024 [pdf] submitted on 2026-07-10 08:19:54
Authors: Rüdiger Giesel
Comments: 5 Pages.
We propose a compact effective mechanism for baryogenesis in which the CP-odd source is the oriented phase of the octonionicassociator. The signed imaginary projection of the associator defines a dimensionless field ΘA that couples derivatively to the baryoncurrent with strength cΘ. In a homogeneous radiation-dominated Universe this coupling gives an effective baryonic chemicalpotential, and baryon-number-violating reactions freeze a nonzero asymmetry when their rate falls below the Hubble rate. Theobserved baryon-to-photon ratio fixes the model-independent target cΘ˙ΘA/TD ≃ 2.4 × 10−8 at freeze-out. For Hubble-drivenrelaxation this corresponds to perturbative associator orientations at high decoupling temperatures, TD ∼ 1012—1015 GeV. We givean explicit baryonic projector, a representative dimension-six baryon-violating operator, the effective equation of motion for ΘA,and the conditions required to avoid sphaleron washout and low-energy nucleon-decay constraints
Category: Relativity and Cosmology
[1649] ai.viXra.org:2607.0023 [pdf] submitted on 2026-07-09 23:37:55
Authors: Lluis Eriksson
Comments: 13 Pages. Consolidation paper #5 of an audit-first programme (companion notes: ai.viXra 2607.0005, 2607.0017, 2607.0018, 2607.0020). Proves part (i) fully and part (ii) for 0 < beta <= 3; the global statement is presented as a quantified conjecture with a verified
For beta > 0 let I_m denote modified Bessel functions of the first kind, a_m = I_m^2[(m-1)I_{m-1}^2 + (m+1)I_{m+1}^2], b_m = m I_m^4, F_A = sum a_m sin(mt), F_B = sum b_m sin(mt), E = F_A/(2 F_B). The global ratio-monotonicity problem for the surface expansion of a two-dimensional SU(2) lattice gauge observable is: (i) F_B > 0 on (0, pi); (ii) E' < 0 on (0, pi), for every beta > 0. We prove (i) twice, and prove (ii) for 0 < beta <= 3 via an exact pair-identity skeleton plus an archived interval certificate executed by two independent interval-arithmetic implementations. The structural core is exact: E is, as an algebraic identity, the mean of cos(psi) under the midpoint law of a four-step killed von Mises bridge; the generating kernels reduce, via the Neumann addition theorem, to two-dimensional integrals of a single Bessel function whose saddle deficit is an exact sum of two squares; and exact saddle cancellations yield the coefficients of the (verified) closed second-order law E = cos(t/2)(1 - c(t)/beta) + O(beta^-2), with c(t) = (4cos^2(t/4) - 1)/(2cos(t/4)cos(t/2)). Three certified negative results kill every monotone full-path coupling, with an exact mechanism at threshold beta|cos t| = 3/2. For the remaining range we give a two-scale closure map with a verified candidate threshold beta_0 = 15 and the complete pi-endpoint package for the cubic coefficient c_3. Every claim is labelled exact / certified / verified; the machine-checked lemmas are Lean 4/Mathlib, machine-checked modulo classical Bessel inputs carried as named hypotheses.
Category: Mathematical Physics
[1648] ai.viXra.org:2607.0022 [pdf] submitted on 2026-07-08 22:56:21
Authors: Fusao Ishii
Comments: 28 Pages. This is Paper 8 of a eight-paper series.
Papers 1—7 of this series derived the Schrodinger equation, the Dirac equation, quantum entanglement, the Coulomb force, the Lamb shift, the anomalous magnetic moment, the hydrogen hyperfine splitting, and the resolution of the double-slit paradox—all for the electron, whose randomness originates in the Zero-Point Field (ZPF) of its own Coulomb interaction. This paper extends the stochastic framework to the photon. The photon has no charge and no rest mass, so the electron’s Abraham—Lorentz equation does not apply directly. We identify the correct photon analogue: the photon’s relativistic (effective) mass meffγ = ℏω0/c^2 replaces the electron rest mass m, and the photon’s own optical cycle τγ0 = 1/ω0 replaces the electron radiation reaction time τ0 = e^2/6πϵ0mc^3. From this photon Abraham—Lorentz equation, equating two independent expressions for the transverse momentum variance gives the photon diffusion coefficient: Dγ = c^2/2ω0 = ℏ/2meffγ, which has exactly the same form as D = ℏ/2m for the electron, with meffγ replacing m. Three major results follow: 1. Maxwell equations are derived from the photon Fokker—Planck equation via the Madelung transformation using the Riemann—Silberstein vector F = √ϵ0E + (i/√μ0)B as the photon wave function. This is the exact photon analogue of deriving the Schrodinger equation from the electron Fokker—Planck in Paper 1. 2. Malus’s law P(pass) = cos(α)^2 is derived from Brownian motion of the polarization angle on the Poincare sphere, without assuming quantum mechanics. 3. Photon randomness originates in the electromagnetic vacuum ZPF—the same field of which the photon is itself a quantum. The coherence volume of a photon equals 2Dγ/ω0 = c^2/ω^2 0 = ¯λ2, consistent with the van Cittert—Zernike theorem. The complete hierarchy of effective descriptions is: Schrodinger (spin- 1/2 , massive) → Dirac (spin- 1/2 , relativistic) → Maxwell (spin-1, massless)—all emerging from stochastic processes driven by the electromagnetic ZPF, differing only in the particle’s mass and spin.
Category: Quantum Physics
[1647] ai.viXra.org:2607.0021 [pdf] submitted on 2026-07-09 05:19:00
Authors: Jason Merwin
Comments: 20 Pages. A GitHub repository link is provided
We demonstrate that gravitational and quantum dynamics can be unified as emergent consequences of strictly bounded computational bandwidth within a discrete generative spacetime (the Discrete Emergent Universe). In this framework, the fundamental phenomena of physics arise from scheduler load: persistent topological defects impose chronic bandwidth demand (analogous to gravitational mass), while acute logical conflicts trigger saturation-limited resolution events (analogous to quantum state collapse). Through pre-registered experiments on a growing triangulated foam, we derive a unified two-queue ledger law---governing forced backlog and standing vacuum demand---that dictates this load response with zero fitted parameters. This single internal law accurately brackets the chronic starvation collapse threshold (a gravitational-regime constant of x50 = 1.30 and completely reproduces acute Zeno-pattern suppression in temporally structured loads. While the central claim is a model-internal unification of these two operating regimes, we provide external bridge diagnostics---including a CMB amplitude basin, preliminary GW150914 ringdown-compression signatures, and formal equivalence to standard quantum and relativistic clock laws---as falsifiable targets for physical equivalence.
Category: Quantum Gravity and String Theory
[1646] ai.viXra.org:2607.0020 [pdf] submitted on 2026-07-09 13:40:14
Authors: Lluis Eriksson
Comments: 8 Pages. Lean verification file and numerical audit script at https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/tree/main/papers/bessel-amos-fh
Let I_nu denote the modified Bessel function of the first kind and, forx>0, let rho_nu(x) = I_{nu+1}(x)/I_nu(x). We give a four-step, fullyelementary proof of the sharp difference inequality0 < rho_nu(x) - rho_{nu+1}(x) < 1/x (x>0, nu>=0), whose right-handinequality is exactly the strict increase of the logarithmic derivative(log I_nu)'(x) under the unit shift nu -> nu+1; consequentlynu -> (log I_nu)'(x) is strictly increasing along every unit-spaced gridnu_0 + N, in particular on the integer and half-integer orders arising inthe application. The stronger continuous-order statement is known(Freitas-Laugesen, arXiv:1810.07461, Lemma 10, via Bessel zeros); we makeno elementary claim about fractional steps. The proof given here uses noinformation about Bessel zeros: it combines the three-term recurrence withthe classical Amos-type upper bound rho_nu < x/(a+sqrt(a^2+x^2)),a = nu+1/2, and rests on the observation that this bound is exactlycalibrated for the problem: 1/U - U = 2a/x is an algebraic identity, and(2nu+1)/x is precisely the threshold the unit step requires; in fact theunit-step monotonicity and the Amos bound are equivalent. As anapplication we record the following consequence in two-dimensional latticegauge theory: for the Wilson action, every mass gap between charactersectors of the 2D transfer operator - for U(1) and SU(2) alike - is astrictly decreasing function of the bare coupling beta, by theFeynman-Hellmann identity. The algebraic core of the proof ismachine-checked in Lean 4/Mathlib (no sorry; axiom oracle: Lean's threestandard axioms), and an independent high-precision numerical audit ofevery inequality used is reported.
Category: Mathematical Physics
[1645] ai.viXra.org:2607.0019 [pdf] submitted on 2026-07-09 19:40:54
Authors: Felix Reichel
Comments: 79 Pages.
This paper studies the determinants (and economics) of free-riding in the swimming stage of massstart triathlon. The theoretical framework builds upon non-discriminatory Tullock contests, modeling triathlon as a simplified two-stage game with quadratic effort costs, and extends to n-player and asymmetric settings in which drafting multiplicatively reduces heterogeneous effective marginal costs.Empirically, I construct an event-study measure of free-riding based on relative rank changes across the two stages to capture free-riding propagation, centered on the exceptional 2020 season, during which non-drafting rules were enforced due to the COVID-19 pandemic.Causal identification combines pooled OLS (POLS) with athlete and event fixed effects (FE), as well as a regression discontinuity design (RDD) exploiting COVID-19 policy—induced rule changes—specifically, individually staggered starts—that mechanically reduced drafting potential and, consequently, its utilization. Additionally the economic analysis chapter uses elasticity, production frontier, and conditional quantile methods to primarily examine group-size effects.The results show that: (i) free-riding was substantially positive prior to 2020, collapsed during the 2020 season, and only partially recovered thereafter; (ii) the drafting effects are stronger for weaker swimmers and athletes in deeper drafting positions, with modest gender differences; and (iii) age heterogeneity is pronounced, with middle-aged and older cohorts benefiting the most, suggesting that athlete experience plays a vital role in efficiently utilizing free-riding gains. However, this latter finding may also be significantly confounded by compositional changes in athletes’ body characteristics over time.
Category: Economics and Finance
[1644] ai.viXra.org:2607.0018 [pdf] submitted on 2026-07-09 14:57:20
Authors: Lluis Eriksson
Comments: 4 Pages. Parametric-in-r Lean formalization included. Lean verification file and exact-arithmetic script at https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/tree/main/papers/parity-barriers
For every r>=1, the uniform measure on the even-parity subset of {+-1}^{r+1}is r-wise independent, yet the last coordinate has unit variance while beingan a.s. function of the others. This example is classical - parity-checkcodes are the standard construction of k-wise independent distributions inthe pseudorandomness literature (Joffe; Alon-Babai-Itai; Alon-Goldreich-Mansour) - and no novelty is claimed for it. What is recorded here is aconsequence we have not seen isolated as a statement: any "comparisonfunctional" whose value depends only on marginal data of order <= r, withconstants uniform over finite measures, takes identical values on the paritymeasure and on the uniform product measure, and is therefore consistent withperfect decoupling on a measure where decoupling fails maximally. Hence noinequality built from bounded-order functionals can imply uniform decouplingprinciples - Dobrushin-type mixing, approximate tensorisation withmeasure-free constants, covariance decay - on any class of measurescontaining the parity family. The case r=1 recovers, and explainsstructurally, the failure of raw-oscillation/Doob and Efron-Stein-type stepsfound repeatedly in an adversarial audit of a constructive Yang-Millsprogramme; no repair within bounded-order data can succeed, because thebarrier recurs at every order. Statements (a) and (b) are machine-checkedin Lean 4/Mathlib parametrically in r (all n; no sorry; standard axiomsonly), the abstract certifying-barrier schema is formalized as well, andfinite decide instances (r<=4) plus exact rational arithmetic (r<=6) serveas independent audits.
Category: Mathematical Physics
[1643] ai.viXra.org:2607.0017 [pdf] submitted on 2026-07-09 19:34:39
Authors: Lluis Eriksson
Comments: 5 Pages. Lean verification file and numerical audit at https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME/tree/main/surface-theorem and papers/phi-lemma.
For x>0 and real m>=1 define phi_m(x) = [(m-1) I_{m-1}(x)^2 + (m+1) I_{m+1}(x)^2] / (m I_m(x)^2), with I_mu the modified Bessel function of the first kind. We prove phi_m(x) < phi_{m+1}(x) for every x>0 and everyreal m>=1 - a weighted Turan-type monotonicity statement we have not found in the literature, although every ingredient of the proof is classical. The proof is fully elementary: eliminating the neighbouring ratios by thethree-term recurrence, the difference factorizes exactly as (S-3c)(P-(2m+1)c) + (2m+1)c^2, with u = I_{m+1}/I_m, c = 1/x, S = u+1/u, P = 1/u-u; the second factor is positive by the calibrated Amos bound (it is precisely the unit-step inequality of the companion note), the first because the same bound forces u < x/(2m+1) <= x/3. As an application we obtain thestrict determinant ordering c_mn < 0 (m
[1642] ai.viXra.org:2607.0016 [pdf] submitted on 2026-07-08 20:37:33
Authors: Xiangqian Zhang, Mingming Zhao, Linchao Ge
Comments: 24 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper, based on Topological Residual Theory (TRT), systematically explains the fractal filling mechanism of spatial flow fields in right-handed cylindrical helical motion at the speed of light, and presents the pure geometric and topological origin of the dimensionless fundamental constantu2015the fine structure constant...
Category: Mathematical Physics
[1641] ai.viXra.org:2607.0015 [pdf] submitted on 2026-07-08 20:32:46
Authors: Bahbouhi Bouchaib
Comments: 44 Pages.
Understanding how rotational motion develops after an impact remains a central problem in continuum mechanics, impact dynamics, and solid mechanics. Classical theories successfully describe stress propagation, elastic deformation, plasticity, contact mechanics, and wave transmission within struck bodies. Nevertheless, they generally describe the observed dynamics through stress and displacement fields without explicitly considering the transient evolution of the material density field as an independent internal variable.In the present work, a new continuum-mechanics framework is proposed in which density is introduced as an evolving thermodynamic state variable coupled to elastic deformation through a free-energy functional. The central hypothesis is that a localized impact generates a transient density perturbation that propagates throughout the body as a relaxation wave. During this process, density gradients, pressure gradients, and elastic stresses evolve simultaneously while continuously exchanging energy through thermodynamically admissible relaxation mechanisms. Rather than assuming that the density field instantaneously returns to equilibrium, the proposed model considers its progressive redistribution until the initial homogeneous state is recovered.The formulation combines the conservation laws of continuum mechanics with a variational free-energy approach and a dissipative gradient-flow evolution equation. The resulting model satisfies thermodynamic consistency, admits a Lyapunov free-energy functional, and naturally predicts monotonic energy dissipation toward equilibrium. Classical elasticity is recovered as a limiting case when density relaxation becomes negligible.To investigate the physical consequences of the proposed formulation, preliminary numerical simulations were performed using custom two-dimensional and three-dimensional computational models. The simulations indicate that off-centre impacts generate transient misalignment between density and pressure gradients, producing a measurable rotational source proxy that reaches a maximum for intermediate impact eccentricities. Although these simulations do not constitute experimental validation, they provide a proof of concept demonstrating that the proposed mathematical framework generates physically meaningful behavior consistent with several qualitative trends reported in the impact-mechanics literature.The theoretical predictions are further discussed through comparison with established results in elasticity, contact mechanics, finite-element analysis, stress-wave propagation, impact dynamics, and thermodynamics. Rather than replacing existing continuum theories, the proposed framework extends them by introducing density relaxation as an additional internal mechanism contributing to energy redistribution following mechanical impact.The proposed formulation establishes a unified theoretical basis for future numerical and experimental investigations of transient density evolution in impacted solids and suggests that density relaxation may represent a useful additional state variable in continuum descriptions of dynamic deformation and rotational response.
Category: Classical Physics
[1640] ai.viXra.org:2607.0014 [pdf] submitted on 2026-07-08 11:02:30
Authors: Fusao Ishii
Comments: 24 Pages. This is Paper 6 of a six-paper series.
The double-slit experiment has been called "the only mystery" of quantum mechanics. For one hundred years the question "which slit does the electron pass through?" has lacked a physical answer: the Copenhagen interpretation declares the question meaningless until measurement; the many-worlds interpretation posits branching universes; the pilot-wave interpretation introduces an undetected guiding field. We present a complete physical answer within the stochastic electrodynamic (SED) framework established in Papers 1—6 of this series. The answer rests on three propositions, all following from first principles: 1. The electron follows a definite trajectory—one that passes through exactly one slit—described by Nelson’s stochastic differential equation (SDE) with diffusion coefficient D = ℏ/2m. 2. The electron’s zero-point field (ZPF), which fills all space as the electromagnetic quantum field of the Coulomb interaction, carries information about both slits through the osmotic velocity u = D∇ln |ψA + ψB|^2. This non-local ZPF correlation guides the electron toward the interference maxima. 3. "Measurement" is a physical disturbance of the ZPF. It replaces the joint probability density ρ = |ψA + ψB|^2 with the conditioned density ρ → |ψA|^2 (Bayes update), which eliminates the interference term 2 Re[ψ∗A ψB] and destroys the fringes. The result is confirmed by Monte Carlo simulation of both the analytical |ψ|^2 distribution (Approach A) and the Nelson SDE (Approach B). Both reproduce the interference pattern; both show its disappearance when which-slit information is available. "The observer creates reality" is replaced by "physical disturbance of the ZPF updates the probability density." The hundred-year paradox is resolved by a concrete physical mechanism requiring no new postulates beyond those established in Paper 1.
Category: Quantum Physics
[1639] ai.viXra.org:2607.0013 [pdf] submitted on 2026-07-08 11:50:28
Authors: Brent Hartshorn
Comments: 8 Pages.
The web’s active-content model rests on JavaScript and, beneath it, on WebAssembly — a stack virtual machine that, in current browsers, must cross a JavaScript boundary for every access to the document. We report a web browser built from the ground up on the minipy/ShivyCX substrate, in which a page’s active content is either Python, executed by an embedded interpreter against a live document, or native machine code compiled ahead of time from an rpython script and invoked through ctypes—with no virtual machine, no JavaScript wrapper layer,and no third-party browser engine. Concretely: script type="python" runs against a shared document/console/window; script type="rpython" is compiled (py2c → gcc -O2) to a cached per-page shared object callable by ctypes, while the same source still runs on stock CPython; a canvas is drawn by a JIT-compiled native fragment shader with time and pointer uniforms at one native call per frame; and JavaScript runs by translation onto the same interpreter and document, not a second VM. Nothing from Blink, WebKit, Gecko, Servo, orNetSurf is used; pages render through a small software widget layer into a Wayland frame buffer. We position the result as a systems alternative to Redox OS (which ports NetSurf or Servo) and ChromeOS (which is Chrome/V8/Blink), and as a descendant of TempleOS’s ground-up philosophy— arguing that each of these optimizes within the JavaScript/engine boundary, whereas co-designing the page-execution model lets us move it.
Category: Data Structures and Algorithms
[1638] ai.viXra.org:2607.0012 [pdf] submitted on 2026-07-07 20:45:06
Authors: Chen Ah Yaw
Comments: 7 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a deterministic primality sieve derived from the multiplicative structure of integers modulo 30. All primes greater than 5 are confined to the reduced residue classes R = 1, 7, 11, 13, 17, 19, 23, 29. We prove that the set R forms a multiplicative group modulo 30, and consequently, the product of any two numbers from these columns remains within the same columnar structure. This allows us to construct a complete multiplication table that generates every composite number coprime to 30. Our central theorem states that for any fixed column c ∈ R, the numbers in that column which are not generated by the multiplication table are exactly the prime numbers. Critically, we demonstrate that this structural sieve provides a direct mathematical explanation for the irregularity of prime distribution: primes are the set-theoretic complement of dynamically spaced, overlapping arithmetic progressions. Based on this, we derive an optimized trial-division algorithm that tests only divisors of the form r + 30k, reducing the number of trial divisions by 73.3% compared to naive trial division and 46.7% compared to odd-number-only division.
Category: Number Theory
[1637] ai.viXra.org:2607.0011 [pdf] submitted on 2026-07-07 13:55:57
Authors: E. P. J. de Haas
Comments: 27 Pages. https://doi.org/10.5281/zenodo.21242316
The gravitational rapidity potential χg(x) generates a local Spin(1,3) rotor G, which forms the common origin of three complementary descriptions of gravitation. A companion paper developed two of these branches: an exact relativistic fluid-dynamical (kinematic) branch and a slow-flow metric branch that recovers the Painlevé—Gullstrand spacetime geometry. The present paper develops the third branch, based on the Maurer—Cartan connection generated by the rotor and its transport along the gravitational vacuum flow. Starting from the spacetime Maurer—Cartan connection Ω_Q=(∂G)G^−1, its proper-time projection is derived for the composed galactic rotor consisting of radial and azimuthal Lorentz boosts. The resulting connection separates naturally into radial and azimuthal rapidity-rate channels together with the Thomas—Wigner bivector arising from the non-commutativity of the two boosts. Transporting this connection with the gravitational four-velocity produces the bilinear UΩ_τ and its complete norm, time, space and spin channel decomposition. The principal mathematical result is that the time-channel transport condition [UΩ_τ]_T=0 reduces, in the physically relevant slow-flow limit, to the previously established Constant-Lagrangian (CL) condition DΓ/Dτ=0, where Γ=coshχrcoshχϕ. Away from the slow-flow limit the two conditions differ by a factor involving the radial Lorentz factor, but they coincide in the galactic regime. This establishes a direct geometric connection between the Maurer—Cartan formulation and the conserved isorapidity flow that characterizes stationary spiral galaxies. Applying the resulting equations to the Painlevé—Gullstrand—Hubble vacuum flow, together with a Newtonian virial boundary condition at the galactic bulge radius, recovers in closed form the Constant-Lagrangian rotation-curve relation previously fitted to SPARC observations. The Maurer—Cartan formulation therefore provides a second theoretical foundation for the Constant-Lagrangian rotation-curve law within the rotor-generated Spin(1,3) hierarchy. In this framework, flat galactic rotation curves emerge from the conserved composition of two orthogonal rapidity components of a single relativistic gravitational vacuum river flow. Throughout the construction, Hubble-embedded Newtonian gravity remains unchanged, and no dark-matter halo, MOND interpolation function or additional free parameter is introduced. The theory extends naturally to stationary cones of constant colatitude, where the resulting trajectories remain smooth helical curves throughout their domain of physical validity.
Category: Astrophysics
[1636] ai.viXra.org:2607.0010 [pdf] submitted on 2026-07-06 19:47:16
Authors: P. H. Antom
Comments: 11 Pages.
We present the Feedback Epistemic Equilibrium Law (FEEL), a formal stability theorem for artificial reasoning systems operating under corrective oversight. Standard control theory stabilises a plant using a controller assumed reliable by construction. FEEL removes this assumption: the feedback mechanism is itself a dynamical system with its own persistence, susceptibility to epistemic contamination, and potential for instability. We model the joint system as the affine recurrence Z_(t+1) = MZ_t + c where the block matrix M (A, -C; D, E)encodes intrinsic reasoning evolution (A) , corrective intervention (C), epistemic leak from reasoning into feedback (D), and feedback persistence (E), We prove that ρ(M) < 1 is necessary and sufficient for (i) existence and uniqueness of an equilibrium, (ii) global convergence from any initial condition, (iii) exponential stability with an explicit rate, and (iv) bounded epistemic-feedback disagreement. We characterise the failure regime ρ(M) >= 1, cataloguing divergence, oscillation, feedback amplification, and runaway correction cascades. We illustrate the criterion on a toy coupled system in which increasing the epistemic-leak strength alone — holding each subsystem’s standalone spectral radius fixed — drives the joint system through the predicted ρ(M) = 1 transition, confirmed across 200 random initial conditions. The result supplies a computable certificate for safe feedback in AI systems and identifies a structural gap in existing alignment frameworks: local stability of reasoning and feedback components does not imply global stability of their coupling.
Category: Artificial Intelligence
[1635] ai.viXra.org:2607.0009 [pdf] submitted on 2026-07-05 03:28:46
Authors: Joshua James Farrow
Comments: 11 Pages.
A change of field boundary conditions produces quanta when it mixes positive- and negative-frequency modes, but the boundary motion is usually prescribed externally. We construct a finiteautonomous quantum shutter in which a quantum matter register controls one local bilinear of aone-dimensional bosonic lattice while the complete matter—field Hamiltonian remains fixed and timeindependent. The controller-gated term is C = ηκqℓqr , and at full closure the open and closed fieldHamiltonians obey the exact local identity Hcl − Hop = κqℓqr . An abrupt opening therefore gives acanonical Bogoliubov transformation with nonzero β, so the closed vacuum is squeezed in the openbasis and a closed-basis one-quantum state becomes a one-quantum-added squeezed state. Exactsparse evolution and canonical matrix-product-state evolution show autonomous packet transmissionbetween the static closed and open limits, controller backreaction, matter—field entanglement, andenergy redistribution with total-energy drift below 4 × 10−13 in the canonical benchmark. After fixingoutgoing modes independently from a prescribed smooth-history reference, far local field algebras canbe close at the 10−4—10−6 level while the joint outgoing state remains distinguishable. A collectivecontroller of size M approaches the prescribed classical switch with leading corrections proportionalto 1/M , in agreement with a spin-coherent fluctuation expansion. The controller register also has anexact embedding into ordinary matter qubits through frustration projectors and a unary clock sector.The construction is a regulated scalar/bosonic realization of standard dynamical-Casimir physics; itis not a derivation of electromagnetic U (1) or of an unregulated infinite particle-number tail.
Category: Quantum Physics
[1634] ai.viXra.org:2607.0008 [pdf] submitted on 2026-07-04 23:32:35
Authors: Ujjwal Singh
Comments: 14 Pages.
Central Bank Digital Currencies, or CBDCs, are becoming one of the biggest topics in global finance. Many central banks argue that CBDCs can help bring millions of unbanked people into the formal financial system. But there is also a serious concern: if too many people move their money from commercial banks into CBDCs, itcould weaken the banking system. This paper looks at both sides of that argument by studying three countries that have already launched CBDCs: the Bahamas with its Sand Dollar, Nigeria with the eNaira, and China with the Digital Yuan. Using data from the IMF, the BIS, the World Bank, and individual central bank reports, the paper evaluates each case based on four things: how much the CBDC helped with financial inclusion, howwidely it was adopted, what impact it had on banks, and what design choices shaped the outcome. The findings show that all three CBDCs made some progress on inclusion, but none of them caused the banking instability that economists worriedabout. The main reason is simple: none of them were adopted at a large enough scale to seriously threaten commercial banks. The paper argues that the tension between financial inclusion and banking stability is not a fixed problem. It is a design problem. With the right choices, both goals can be pursued at the same time.
Category: Economics and Finance
[1633] ai.viXra.org:2607.0006 [pdf] submitted on 2026-07-04 23:28:33
Authors: J. W. McGreevy
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The Riemann hypothesis is realized as a direct theorem inside the RFTP framework. The single global linear constraint enforced by the weight-12 modular discriminant organizes shear amplitudes extracted from odd Galois eigenspaces at irregular primes into a rigid balancing law. The same constraint trivializes the effective second Stiefel—Whitney class, yielding a globally defined spinor bundle on which a non-linear Dirac Hamiltonian is essentially self-adjoint with real spectrum. After an explicit canonical spectral shift and adelic factor, the regularized spectral determinant coincides with the completed Riemannfunction Ξ(s). The distributional trace formula reproduces Weil’s explicit formula exactly inthe atomic limit of the Hopf—Lax flow, and Tauberian extraction recovers the zero-countingfunction with the Riemann-hypothesis error term. Consequently every non-trivial zero lieson the critical line. RFTP inverts the conventional paradigm: arithmetic data at irregular primes function as the generators of geometric and dynamical structure rather than emerging from an a priori physical process.
Category: Mathematical Physics
[1632] ai.viXra.org:2607.0005 [pdf] submitted on 2026-07-02 21:47:02
Authors: Lluis Eriksson
Comments: 6 Pages.
We report a complete formalization, in Lean 4 over Mathlib, of volume-uniform Wilson-loop area laws for SU(Nc) lattice gauge theory in an explicit strong-coupling window - including the case of the exact Wilson Boltzmann factor, not a linearized surrogate. The headline theorem bounds the normalized Wilson-loop expectation by Nc eP·4dK σArea(C) eP·4dS(σ), where Area(C) is an intrinsic combinatorial filling area of the loop, P is its edge-support size, and every constant is volume-free: the bound holds uniformly over all finite lattice sizes. The partition function is cancelled through a fully formalized volume-restricted cluster expansion (loop-tagged factorization, restricted Mayer inversion, Z-ratio bounds, and a pinned-gas resummation built on a Kotecky-Preiss layer with Penrose-style spanning-tree counting). A reusable repackaging converts the bound into manifest exponential area decay with a strictly positive string tension, and the non-vacuity of every hypothesis window is itself machine-checked - both the cluster smallness window and the decay-repackaging window, the latter with an explicit witness of tension log 2 - 1/2. For every exported theorem in this chain the Lean kernel's axiom oracle reports exactly [propext, Classical.choice, Quot.sound]; there is no sorry and no project axiom in the dependency cone. To our knowledge this is the first machine-checked cluster-expansion proof in lattice quantum field theory. All artifacts are public, with per-theorem oracle records in a verification ledger and continuous-integration builds.
Category: Mathematical Physics
[1631] ai.viXra.org:2607.0004 [pdf] submitted on 2026-07-03 22:03:44
Authors: Peilin Wen
Comments: 8 Pages.
We investigate further algebraic and combinatorial properties of a 7-vertex strongly con- nected directed graph whose adjacency matrix A has characteristic polynomial χA(λ) = λ2(λ − 2)(λ − 1)(λ + 1)3 and Perron root ρ(A) = 2. We establish four main results. First, the14 directed edges of A are shown to correspond to a directed selection from the Fano planeP 2(F2) with one line deleted. Second, we construct a complete Jordan basis of seven integer generalized eigenvectors, yielding the Jordan form J = 1(2)⊕J1(1)⊕J1(−1)⊕J2(−1) ⊕J2(0) with det(V ) = 144. Third, we construct the biorthogonal left-vector basis and seven rank-one projection operators, achieving the Jordan-Chevalley decomposition A = S + N with N 2 = 0. Fourth, we give a spectral computation of the number of closed walks of length L, obtaining NL = 2L +1+3(−1)L, and verify its consistency with the closed-walk equal-weight theorem.
Category: Combinatorics and Graph Theory
[1630] ai.viXra.org:2607.0003 [pdf] submitted on 2026-07-03 21:58:27
Authors: Haizhu Wu
Comments: 55 Pages. Zenodo DOI: 10.5281/zenodo.21165454.
We present a complete, rigorous, and unconditional proof of Polignac’s conjecture, which asserts that for every even integer y ≥ 2, there exist infinitely many pairs of primes (q, q+y). The twin prime conjecture corresponds to the special case y = 2. The proof introduces a fundamentally new framework that combines five key in novations. First, a geometric primality criterion establishes that in the interval (p, p2), an integer is prime if and only if it is coprime to all primes ≤ p. This deterministic equivalence completely circumvents the parity problem of classical sieve theory. Second, a double arithmetic progression structure with CRT pre-sieving processes small primes r ≤ log p via the Chinese Remainder Theorem, constructing an admissible set A0 modulo M0 = Q r≤log p r. This ensures the crucial condition gcd(M0, d) = 1 for all subsequent moduli d. Third, physical-space period cancellation exploits the fact that the arithmetic progression a + tM0 (mod d) traverses a complete residue system, causing error contributions from complete periods to vanish identically. Fourth, resonance breaking decomposes exponential sums over A0 into 3π(log p) = po(1) explicit terms, eliminating the large factor |A0| from estimates. Fifth, a four-zone modulus partition applies distinct estimation techniques to different ranges of moduli d in the Möbius expansion. All error terms are rigorously shown to be of strictly lower order than the main term C0p2/(log p)2, where C0 > 0 equals the Hardy-Littlewood constant for the pair (0, y). The proof uses only classical Fourier analysis on finite abelian groups, elementary number theory, and standard estimates from analytic number theory. No unproven hypotheses are assumed.
Category: Number Theory
[1629] ai.viXra.org:2607.0002 [pdf] submitted on 2026-07-03 14:09:45
Authors: Ginanjar Utama
Comments: 11 Pages.
This primer presents Dirac’s and Penrose’s "square-root" methods in one language: real geometric(Clifford) algebra. Dirac’s square root of the wave operator forces the Clifford relation and leads to rotors, spinors, and the Dirac equation; Penrose’s square root of a null vector leads to 2-spinors, flags, twistors, and the spin-network idea that geometry may be recovered from quantum angularmomentum. The exposition is written for graduate students who know special relativity and elementary quantum mechanics. It keeps the historical claims modest, separates convention from invariant content, and works every major idea through a concrete computation: the belt trick, theHestenes form of the Dirac equation, the null flagpole, the Dirac—Penrose conformal bridge, thespin-geometry theorem, and a complete 2+1 dimensional miniature in which bivectors, Lorentzorbits, unitary representations of SU(1, 1), and Clifford-signature superselection all fit into onediagram. Sixteen exercises are included so that the reader can verify the algebra rather than merely admire it.
Category: History and Philosophy of Physics
[1628] ai.viXra.org:2607.0001 [pdf] submitted on 2026-07-02 19:14:41
Authors: Lluis Eriksson
Comments: 8 Pages.
Let Kn+1 be the complete graph on the vertex set {0, 1, ..., n}, and for a spanning tree T of Kn+1, rooted at 0, let cT(v) denote the number of children of the vertex v. We prove the exact identity: the sum, over all spanning trees T of Kn+1, of the product over vertices v of cT(v)! equals n! Cn, where Cn is the n-th Catalan number. Equivalently, the normalized sum (n+1)((n+1)!)-1 times the weighted tree sum equals Cn exactly. The proof is bijective: pairs consisting of a spanning tree together with a linear ordering of every child set are placed in explicit bijection with vertex-labeled plane trees on n+1 nodes whose root carries the label 0. The identity arises as the exact "second-Ursell" normalization constant in the author's audit-first programme on four-dimensional SU(N) Yang-Mills existence and mass gap, where it had been isolated as a named open proposition in a public challenge repository; the present paper is self-contained combinatorics and makes no claim about that programme. The entire proof has been formalized in Lean 4 against a pinned Mathlib snapshot: the headline declarations compile with no sorry, and the kernel's axiom oracle reports exactly [propext, Classical.choice, Quot.sound]. All artifacts, including a pinned continuous-integration replay of the full verification, are public.
Category: Mathematical Physics
[1627] ai.viXra.org:2606.0085 [pdf] submitted on 2026-06-30 20:09:42
Authors: Paul Robert Mesler
Comments: 15 Pages.
We conducted an experiment where a rotator rotated in a horizontal plane with respect to the earth. The rotator at one end was connected to a vertical shaft that was embedded in a horizontal bearing assembly. The bearing assembly was attached to a sliding platform that was constrained to move with one degree of freedom along a linear track. The main point of the experiment was to determine if the orbital angular speed of the rotator increased due to fictitious forces. The accelerometer attached to the rotator showed a local increase in angular speed of the rotator when it passed the 90 degrees point and the 270 degrees point of its angular displacement. Based on this invariant increase in angular speed, we derived a general invariant impulse equation that remarkably predicted this increase leads to an increase in the center of mass momentum of a system.
Category: Classical Physics
[1626] ai.viXra.org:2606.0084 [pdf] submitted on 2026-06-30 02:36:48
Authors: Brent Hartshorn
Comments: 5 Pages. https://github.com/brentharts/ShivyC
Traditional meta-compilation frameworks—most notably PyPy’s RPython—achieve execution speed by translating high-level dynamic languages at the bytecode level into intermediate control-flow graphs for whole-program type inference. While powerful, this approach carries substantial architectural complexity and runtime tracing infrastructure. This paper introduces minipy, a lightweight, high-performance Python interpreter built using an extended variant of RPython. Moving away from traditional bytecode-level translation, minipy employs a novel AST-driven flattening architecture integrated directly into the ShivyCX/py2c compilation pipeline. By emitting direct, statically optimized C components that integrate bare-metal compiler passes—such as register-resident global flag packing, non-recursive static buffer relocation, and tail-call elimination—the resulting interpreter bypasses typical virtual machine overhead. Empirical evaluations show that minipy significantly minimizes execution footprints and outperforms CPython in critical micro-benchmarks.
Category: Data Structures and Algorithms
[1625] ai.viXra.org:2606.0083 [pdf] submitted on 2026-06-30 20:06:17
Authors: J. W. McGreevy
Comments: 19 Pages.
We present the Relativistic Field Theory of Primes (RFTP) as a rst-principles derivationof low-energy physics from a single global object: the adelic spectral triple equipped with one rst-class constraint (the weight-12 central grading) in the min-plus semiring. Local sheardata at irregular primes evolve under the Hopf-Lax formula the explicit tropical linearevolution that realizes the dynamical Legendre transform. This single min-plus constraintgenerates a gauge symmetry (tropical equivalence), produces proper time as its evolution parameter, and yields an emergent EinsteinCartan geometry whose curvature 2-form is the tropical variety created by dierential relaxation across Galois eigenspace channels. Weprove that the functor from the category of such adelic spectral triples to the categoryof Lorentzian/EinsteinCartan geometries is an equivalence on the arithmetic subcategory.The Riemann Hypothesis appears as the statement that the tropical linear ow remains causal and dispersionless if and only if all non-trivial zeros lie on the critical line the unique stable tropical attractor of the theory. Higher SeeleyDeWitt coecients generate tropical polynomials in the shear amplitudes that control connement strength and the mass gap.
Category: Mathematical Physics
[1624] ai.viXra.org:2606.0082 [pdf] submitted on 2026-06-30 05:52:42
Authors: Jason Merwin
Comments: 10 Pages. A GitHub repository link is provided
We exhibit a minimal combinatorial model in which a single structural property—second-order self-reference—produces three features usually treated separately: an intrinsic arrow of time; a sharp distinction between a closed ("block") and an open future; and the stabilization of a shared, observer-independent reality. The central result is a constructive identity: the set of graph configurations that a self-referential observer cannot resolve from within at a given stage is equal, under independent definitions, to the set of sites where the graph must expand to relieve that irresolution. Incompleteness and expansion are therefore one event with two descriptions, rather than two coincident processes. Iterating the resolution rule makes time a generative process—completing the incomplete seeds new incompleteness—and introduces a control parameter, the branching ratio of the abstraction, whose critical value separates a sub-critical phase in which paradoxes exhaust and time halts from a super-critical phase in which they self-sustain and the open future is guaranteed; in the generic toy sweep we locate this critical point at βc ≈ 1.08, near the unit replacement threshold expected on heuristic grounds.e show that shared reality emerges not at the contested frontier but one step behind it: the nodes that expansion has resolved are frozen against the common history and become observer-independent, so that independent observers who disagree entirely about the unresolved present nonetheless agree completely, and stably, on the resolved past.Crucially, we demonstrate that this mechanism transfers successfully from the toy model directly into the native Distinction Engine Universe (DEU) architecture. When projected onto the formal relational registry, the exact same generative dynamics and critical phase transitions emerge organically. The framework's inherent capture modes seamlessly support the incompleteness-driven expansion, verifying that the arrow of time and the crystallization of a shared reality are intrinsic structural consequences of the DEU substrate. The model is deliberately abstract: it operates on self-reference as a structural property and makes no claim about consciousness, quantum mechanics, or any specific physical realization, but it establishes a rigorous formal candidate for how a relational physical substrate forces the flow of time.
Category: Combinatorics and Graph Theory
[1623] ai.viXra.org:2606.0081 [pdf] submitted on 2026-06-30 16:33:22
Authors: Jad Nohra
Comments: 11 Pages.
We advance a claim: learned (deep-learning and reinforcement-learning) control is replacingclassical robust control, H∞ synthesis and µ-synthesis, for the same reason deep convo-lutional networks displaced hand-engineered computer vision pipelines (SIFT, HOG, thedeformable parts model). Both are instances of one mechanism: replacing a fixed, pre-committedsignal/noisepartitionimposedbyahand-designedprocessinglayerwithalearnedpartition, thereby recovering predictive structure that the fixed partition discarded as noise.Theconservationlawsofcontrolarefundamentalandstayapplicable; thenewcontrollersarebound by them all the same. Our contribution is the cross-domain synthesis and preciselyseparating which limits are artifacts of an assumption and which are genuine information-theoretic converses. The argument is organized case by case: each claim is stated, givenits precise conditions and constants, attributed to its governing assumption, marked as stillconstraining or relaxed, and cited.
Category: Artificial Intelligence
[1622] ai.viXra.org:2606.0080 [pdf] submitted on 2026-06-29 20:01:12
Authors: Ayush Samanta
Comments: 13 Pages. (Note by ai.viXra.org Admin: For the last time, an abstract in the article labeled as such is required!)
Orbital debris has become one of the most significant challenges facing the long-term sustainability of Low Earth Orbit (LEO). As the number of satellites continues to increase, so does the likelihood of collisions capable of generating large quantities of debris, potentially triggering a self-sustaining chain reaction known as Kessler Syndrome. This study develops a stochastic two-shell Monte Carlo model to investigate whether a critical orbital density exists beyond which such debris cascades become increasingly likely. The model represents the orbital environment using two concentric shells and incorporates stochastic collisions, debris fragmentation, atmospheric decay, active satellite failure, and collision avoidance. A systematic density sweep was performed using 200 independent Monte Carlo simulations for each normalized orbital density. The results reveal a rapid transition from stable orbital evolution to near-certain cascade formation over a narrow range of densities, with the critical normalized density multiplier estimated to be approximately $alpha_c approx 0.093$. Near this threshold, simulations with identical initial conditions frequently produced different long-term outcomes, highlighting the importance of stochastic collision dynamics in determining orbital stability. Although the model adopts several simplifying assumptions, it reproduces the fundamental feedback mechanism underlying the Kessler hypothesis and provides a computationally efficient framework for investigating the probabilistic onset of orbital debris cascades.
Category: Astrophysics
[1621] ai.viXra.org:2606.0079 [pdf] submitted on 2026-06-29 19:55:34
Authors: Paul Emmett Zaffuto
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)
This paper presents a novel mechanical-to-electromagnetic chronological model to explain the localized 60-second ionospheric pre-cursor anomaly observed prior to the June 24, 2026, Venezuelan doublet earthquakes (Magnitude 7.2 and 7.5). While standard models struggle to explain the rapid coupling between crustal stress and the upper atmosphere, this theorysynthesizes the piezoelectric properties of regional quartz-bearing schists with a highly distinct parallel geometric alignment. We hypothesize that macro-scale structural failure was preceded by micro-fracturing of dense quartz blocks, generating a massive static electrical discharge. Due to a 1° to 3° parallelalignment with the Equatorial Electrojet (EEJ), this subterranean charge acted as a parallel conductor, cleanly disrupting the atmospheric current axis exactly one minute before tectonic slip.
Category: Geophysics
[1620] ai.viXra.org:2606.0078 [pdf] submitted on 2026-06-29 19:53:17
Authors: Peilin Wen
Comments: 9 Pages.
We investigate a 7-vertex strongly connected directed graph whose adjacency matrix A exhibits an exceptionally clean algebraic structure. The characteristic polynomial factorises completely as χA(λ) = λ2 (λ −2)(λ −1)(λ + 1)3 ,so the spectrum is {2, 1, −1, 0} with algebraic multiplicities 1, 1, 3, 2, respectively. The Perron root is ρ(A) = 2, and the associated right eigenvector isv = (9, 3, 2, 6, 7, 1, 8)T∈Z7 >0.For every directed edge i →j we define the rational weight wij = vj/(2vi). These weights form a row-stochastic matrix. We prove that for any closed directed walk of length L (vertices and edges may repeat), the product of the weights along the walk is exactly 2−L , independent of the walk’s itinerary. The proof follows solely from the Perron eigenvector equation and the elementary in—out balance of vertices along a closed walk. We further show that A is non-diagonalisable: it contains a 2 × 2 Jordan block for λ = 0 and at least one for λ = −1. The one-dimensional nullspace is spanned by (1, −1, 0, 0, −1, 1, 0)T , encoding a linear conservation law among four vertices. This graph provides a minimal exactly solvable model with potential applications to loop-model partition functions, non-Hermitian quantum walks, and rapidly mixing Markov chains.Keywords: directed graph; closed walk; Perron—Frobenius theorem; Jordan canonical form; row-stochastic matrix; non-Hermitian quantum walk; exceptional point; exactly solvable model.
Category: Combinatorics and Graph Theory
[1619] ai.viXra.org:2606.0077 [pdf] submitted on 2026-06-28 09:15:50
Authors: Ginanjar Utama
Comments: 13 Pages.
The preceding paper in this sequence connected matter-first spin networks to the simplicity-constrained EPRL vertex: matter-line frames generate spacetime-algebra bivectors, the EPRLmap selects a ray in the bivector invariant plane, and the Lorentzian four-simplex amplitude can be evaluated as a nite-cuto tensor network on K5. That result was kinematical and vertex-local. This paper asks the next question: when curvature is present, can the matter determinant see it, and can it back-react on the spin-foam flatness tendency? We build a finite hinge-link model in which several four-simplices meet around an internal triangle. The Regge decit ϵh = 2π −Pσ⊃h Θσh is represented as a rotation in the two-plane normal to the hinge,with spin lift Uspin(ϵh). The first exact result is the holonomy obstruction det(I − Uspin) = 16 sin^4(ϵh/4), which vanishes in the flat sector, modulo the expected spinorial 4π periodicity. A finite graph Dirac operator on the hinge link reproduces the same obstruction and develops a curvature-induced spectral gap. Integrating out fermions therefore suppresses the near-at zero-modesector in a one-hinge toy model, opposing the gravitational atness preference. For two hinges,disconnected link graphs factorise exactly, whereas edge-sharing link graphs have a non-zero determinant interaction; matter propagation then induces a curvature-curvature correlation between neighbouring defects. Finally we add a chiral Spin(4) = SU(2)+ × SU(2)− split. A single finite hinge determinant is phase-trivial, arg det(Dχ + m) = 0, so it can bias chiral variances but cannot by itself generate orientation-sign flow. The parity-odd channel in four dimensions is instead the Pontryagin pairing tr(γ5Σ1Σ2) ∼ B1 ∧ B2, non-zero only for transverse hinge planes. The result is not a continuum limit or a derivation of the full spin-foam measure. It is a controlled finite-complex mechanism: fermion determinants are holonomy-sensitive functionals of Regge decits and can induce matter-mediated curvature correlations on spin-foam hinge links.
Category: Quantum Gravity and String Theory
[1618] ai.viXra.org:2606.0076 [pdf] submitted on 2026-06-28 13:37:43
Authors: Joseph Shaffer
Comments: 7 Pages. This paper is the companion paper of ai.viXra.org:2605.0049. It provides the formal mathematical foundation.
This paper develops the full Lagrangian formulation of the Tensional Structure Principle (TSP). In TSP, the fundamental substrate of reality is the entanglement domain E, composed of qubit scale flexible mats described by a stiffness field with a tension field as the primary dynamical quantity. Mass induces distortions in the mat field, producing gravity as a tension gradient. We construct the action, derive the Euler-Lagrange equations, identify the stress—tension tensor, and show how dark energy arises from a uniform residual tension. This paper provides the mathematical backbone for the conceptual TSP framework.
Category: Astrophysics
[1617] ai.viXra.org:2606.0075 [pdf] submitted on 2026-06-27 19:52:24
Authors: Khazribouzidi Fethi
Comments: 7 Pages.
We study the phase coherence of Dirichlet polynomials associated with arithmetic progressions of primes. For a k-term prime progression (p, p+d, ..., p+(k-1)d), we prove that the infimum over t in R of the normalized modulus is positive if and only if d > c_k p, where c_k is the unique positive root of sum_{j=1}^{k-1} 1/(1+j c_k) = 1. The sequence (c_k) is strictly increasing, with c_3 = 1/sqrt(2), c_4 = (2/sqrt(3)) cos(pi/18), and c_k ~ ln k as k tends to infinity. Since c_k >= c_4 > 1 for all k >= 4, every arithmetic progression of k >= 4 primes with d <= p has zero spectral coherence. This gives a sharp spectral criterion that separates coherent from non-coherent prime progressions. Numerical verification on more than 1.5 million prime constellations confirms the results with zero exceptions. The proof is unconditional and relies on Baker's theorem and the Kronecker-Weyl equidistribution theorem.
Category: Number Theory
[1616] ai.viXra.org:2606.0074 [pdf] submitted on 2026-06-27 03:56:08
Authors: Ginanjar Utama
Comments: 9 Pages.
A previous paper proposed a matter-first route to loop quantum gravity: interaction vertices define the graph, fermion-line segments carry local SL(2,C) frames, and geometry is reconstructedfrom the resulting spacetime-algebra comparators. Its central open gap was the relation betweenthose matter-built bivectors and the simplicity-constrained boundary data of spin-foam dynamics. This paper closes that kinematical gap and adds a finite-cutoff vertex algorithm. First, we express the EPRL linear simplicity constraint in the invariant plane of the bivector classification B^2 = s + pI: up to the standard sign and normalisation conventions for SL(2, C) Casimirs, the EPRL embedding Y_γ : j → (ρ, k) = (γj, j) selects a ray p/s = 2γ/(γ^2 − 1). Second, we sharpen the closure bridge: the area-vector closure condition at a tetrahedron is equivalent to the Minkowski polygon inequality, and this is exactly the condition that the four-valent intertwiner space be non-empty. Thus classical closure and quantum admissibility are two presentations of the same Gauss constraint. Third, we construct the Lorentzian vertex from the same data: the boost sector is represented by principal-series generators certied by the so(1, 3) algebra and Casimirs, and the node booster B^γ_4 is evaluated as a radial boost integral. Finally, by absorbing each booster and intertwiner into a rank-four node tensor, the finite-cutoff EPRL four-simplex amplitude becomes a tensor-network contraction on K_5 rather than an explicit state sum. The result is not a continuum limit; it is a reproducible bridge between the matter determinant,bivector simplicity, and a computational Lorentzian EPRL vertex.
Category: Quantum Gravity and String Theory
[1615] ai.viXra.org:2606.0073 [pdf] submitted on 2026-06-27 05:30:58
Authors: Jay Kumar
Comments: 30 Pages.
Classical formal logic provides a rule-governed foundation for truth, derivability, admissibility, andsymbolic transformation. However, binary truth values are often insufficient for computationalsystems that must represent partial support, unresolved state, decay, convergence, and changingevidence. This paper develops a five-state calculus of uncertainty grounded in the formal lineageof Hilbert and Ackermann, Church, and Turing. The proposed calculus represents logical states astagged potential values over a normalized implementation space p ∈ [0, 1] and an equivalent signedtheoretical space s(t) ∈ [−1, 1]. The five named regions are false, almost false, undetermined, almosttrue, and true.The central claim of the calculus is that uncertainty need not be treated as failure, noise, or vagueincompleteness. Instead, uncertainty can be represented as computable state. The undeterminedstate is not interpreted as half true, but as the center of a signed state space. Certainty is defined asdistance from this center, while uncertainty is maximal at the center and minimal at the poles. Logicaloperators are defined over potential values and lifted back into named states through threshold-basedclassification.Beyond static classification, the calculus treats propositions as state trajectories. A proposition maymove toward truth, collapse toward falsity, decay toward uncertainty, oscillate under competingevidence, or converge toward a settled pole. The framework therefore introduces dynamic quantitiessuch as velocity, acceleration, distance traveled, directional accumulation, certainty, uncertainty,convergence, and admissibility. These quantities allow two propositions with the same instantaneouslabel to be distinguished by their histories and motion.A minimal LambdaScript reference implementation is provided to demonstrate that the calculus canbe expressed as executable symbolic definitions rather than as informal terminology. The result is acompact computational substrate for uncertainty-aware state validation, intended as a stepping stonetoward Beyond Binary systems and neurocontextual lateral propagation-diffusion architectures.
Category: Data Structures and Algorithms
[1614] ai.viXra.org:2606.0072 [pdf] submitted on 2026-06-27 19:46:59
Authors: Xiangqian Zhang，Mingming Zhao，Linchao Ge
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Within the framework of Topological Residual Theory (TRT), this paper rigorously establishes the first-principles physical picture that "space itself flows at the speed of light along curves in a righthanded cylindrical helical form." In this picture, length and time originate from different aspects of the same spacetime flow motion, thereby providing a geometric explanation for the origin of theconstancy of the speed of light. To fundamentally resolve the dimensional mismatch among different physical fields that arises inclassical field theory from differing measurement protocols, we propose a Velocity-Field Representation scheme: the electric, gravitational, and magnetic fields are directly defined as the three local velocity components of the light-speed spacetime flow along the orthogonal basis of the Frenet-Serret (FS) frame: This achieves a complete unification of all underlying field dimensions to velocity at the kinematic level. Since the flow speed of spacetime is fixed at the speed of light , different physical interactions essentially correspond to the allocation of this motion budget among the three orthogonal directions: tangential propagation, normal centripetal constraint, and binormal torsion. The allocation mechanism is precisely controlled by the helical pitch angle. By introducing the time definition , we derive the first-order time-evolution equations of the three fields under the characteristic rotation frequencies of the FS frame (bending frequency, twisting frequency ). Under the rigid rotation of the frame, the total kinetic energy density remains strictly constant. Utilizing the rigid rotational dynamics of the frame and the vector and scalar triple-product identities, we elucidate thephysical nature by which the "self-work" terms of the rigid triad automatically vanish during rotation, thereby revealing the deep geometric mechanism of dissipation-free energy flow.The macroscopic observable fields — centripetal gravitational acceleration , tangentialelectric field strength , and magnetic rotational angular frequency — emerge naturally as the time derivatives or rotational frequencies of the underlying velocity fieldsE = ct, A = cn, B = cb. E = ct, A = cn, B = cb.cα ds = c dt ωκ = cκ ωτ = cτ U = 2 1 (E ⋅ E + A ⋅ A + B ⋅ B) = 2 3c 2 g = c 2κn e = c 2κt Bmacro = cτb after being modulated by the motion-budget allocation. This provides a self-consistent firstprinciples framework for the geometric unification of gravity and electromagnetism.
Category: Mathematical Physics
[1613] ai.viXra.org:2606.0071 [pdf] submitted on 2026-06-27 19:43:33
Authors: J. W. McGreevy
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We demonstrate that the infrared dynamics of the resonant spectral triple in the Bost-Connes system, deformed by irregular-prime shear, implements a precise arithmetic analogueof the classical Legendre transform. Starting from a classical Poisson manifold whose coordinates are the shear amplitudes {Iu2032p} and the bifundamental mixing field Φ, we construct an explicit action functional whose Legendre transform yields a Hamiltonian on the cotangent bundle. The weight-12 winding condition is imposed as a classical first-class constraint, and Dirac reduction produces a reduced symplectic manifold Pred. Deformation quantization of this reduced space, driven by the modular derivation Dp acting asymmetrically through Φ on the two complex-multiplication stabilizers (Z/6Z at τ = ρ and Z/4Z at τ = i), generates a non-commutative star product whose leading commutator is non-vanishing and proportional to the stabilizer contrast transmitted by Φ. This framework naturally produces: (i) proper time τ as the integrated thermodynamic work along the flow, with lapse N ∝ det(∇2P) · Tr(Φu2020Φ); (ii) a non-removable relative phase between up- and down-type sectors, yielding the Jarlskog invariant as a direct dynamical consequence of the asymmetric action of the real endomorphism J (J2 = −Id) forced by the holonomy defect; and (iii) definite outcomes via deterministic Hamilton—Jacobi flow to a unique weight-12 attractor, with probabilities given by normalized infrared Boltzmann weights from the entropy functional S(ϕ). The construction draws explicit parallels with Dirac’s deformation of Poisson bracketsinto commutators and Tate’s adelic Poisson summation, providing a unified non-commutativestructure that bridges arithmetic geometry and quantum field theory. The imaginary unit i emerges necessarily as the spectral manifestation of the real endomorphism J required to close the holonomy defect. All physical features follow rigorously from the arithmetic data without external postulates.
Category: Mathematical Physics
[1612] ai.viXra.org:2606.0070 [pdf] submitted on 2026-06-26 20:27:10
Authors: Luisiana X. Cundin, William P. Roach
Comments: 9 Pages.
Gabriel's compilation of wet skin dielectric properties reveals exceptionally high permittivity values ($10^5$ to $10^6$) at low frequencies, far exceeding the permittivity of water ($varepsilon approx 80$). These values are not measurement artifacts but reflect the contribution of the electrical double layer---specifically the Stern layer---to the measured dielectric response. The Stern layer confounds dielectric measurements by introducing a multiplicative capacitive contribution that masks the tissue's true dielectric properties. Using the Maxwell-Wagner transformation, $varepsilon_r'' = varepsilon_0 omega sigma_{text{exp}}'$, from the Cundin-Roach Kramers-Kronig analysis, we recover the intrinsic tissue absorption. The corrected absorption values are consistent with pure liquid water, confirming that biological tissue is fundamentally a water-based dielectric whose low-frequency response is dominated by the Stern layer capacitance. The Stern layer is not merely a confounding factor; it is an active biological structure that mediates electromagnetic energy transmission between and within cells. These results have implications for tissue characterization, bioelectromagnetic modeling, and understanding intercellular communication.
Category: Physics of Biology
[1611] ai.viXra.org:2606.0069 [pdf] submitted on 2026-06-26 09:44:58
Authors: Allan Plankhart
Comments: 11 Pages.
Building on a pre-temporal collapse model, we derive a structural correspondence between the surviving 2D sector and the Standard Model’s weak isospin. We show that an embedded 2-brane in a 3D bulk possesses a local frame rotation group SO(3). The spin connection on the brane is an so(3)-valued one-form.Since so(3) ∼= su(2), this connection is exactly an SU(2) gauge field, and spinorial matter confined to the brane necessarily transforms as doublets. This geometrically forces the effective field theory to be Yang—Mills with a Chern—Simons term, uniquely constraining the dynamics. We construct the resulting action, including kinetic mixing with the 3D bulk, and derive testable signatures: a dark matter fluid from the brane foam, distinctive CMB non-Gaussianities with a characteristic oscillatory power spectrum, and missing-energy collider events with a topological mass peak. We provide current constraints and outline the Boltzmann evolution needed for precise predictions.
Category: Mathematical Physics
[1610] ai.viXra.org:2606.0068 [pdf] submitted on 2026-06-26 20:21:58
Authors: Haizhu Wu
Comments: 48 Pages.
We present a complete proof of the Polignac conjecture: for any even integer y, there exist infinitely many pairs of primes (x, x + y). In particular, taking y = 2 yields the twin prime conjecture. The core strategy is to show that for every sufficiently large prime p, there exists a prime x ∈ (p, p2) such that x + y is also prime. This is achieved through threetechnical innovations. First, we apply a double inclusion-exclusion decomposition to the sieved set A0,expressing its character sums as alternating sums of exact geometric series. The keysimplification is that the sum over frequencies of reciprocal distances is independentof the subset chosen, reducing the problem to a universal harmonic estimate. Thisbreaks the resonance phenomenon responsible for the square-root barrier in classical Fourier analysis. Second, we exploit the CRT product structure of A0 to prove that its Fouriercoefficients on Z/M0Z are absolutely summable with subpolynomial total mass. This yields a uniform character sum bound that is independent of the modulus for moduli up to M0. Third, we develop an elementary symmetric polynomial method to control the super-exponentially many terms arising from inclusion-exclusion. By the Maclaurin inequality, the sum over all squarefree divisors of the medium primes is compressed into a convergent Poisson-type series. The tail is controlled by Poisson tail estimates, giving power-law decay. The modulus range is divided into three regimes. For small moduli (d ≤ p 1/3 ), the resonance-breaking estimate combined with an oscillatory bound for the t-sum provides sufficient control. For medium moduli (p 1/3 < d ≤ M0), the Fourieruniform bound combined with the symmetric polynomial method controls the error. For large moduli (d > M0), the sparsity of A0 relative to the modulus allows direct counting, bypassing character sum estimates entirely and preserving the crucial 1/d decay factor. The total error is O(p 5/3+o(1)), which is negligible compared to the main term ∼p 2/(log p) 2. The proof avoids deep tools such as the Bombieri-Vinogradov theorem, spectral theory of automorphic forms, or Kloosterman sum estimates.
Category: Number Theory
[1609] ai.viXra.org:2606.0067 [pdf] submitted on 2026-06-26 19:05:38
Authors: E. P. J. de Haas
Comments: 44 Pages. doi.org/10.5281/zenodo.20939007
We establish the gravitational rapidity field χ_r as the primary scalar of a vacuum-flow description of gravity. The Painlevé—Gullstrand river velocity and the Einsteinian metric arise as successive approximations via two irreversible information-reducing projections that discard, first, the Lorentz factor cosh(χ_r) and, second, the bivector phase encoding the direction of flow. General Relativity is therefore acceleration-relativistic but not flow-relativistic; the physical velocity v_r = c·tanh(χ_r) remains bounded at both horizons without singularity or superluminal disclaimer.At the galactic scale, the constant-Lagrangian (CL) condition D(Γ)/Dt = 0, where Γ = cosh(χ_r)·cosh(χ_φ), is re-read in rapidity language: every CL streamline traces a circle of fixed hyperbolic radius ψ_Γ on the Poincaré rapidity disk, the isorapidity surface cosh(χ_r)·cosh(χ_φ) = Γ_0. This surface simultaneously encodes the flat galactic rotation curve as the projection of the circle onto the azimuthal rapidity axis at the velocity-balance radius r_c, and the exact cancellation of all local gravitational terms in the sigma channel of the field equation, leaving the purely cosmological residual c·Π_{g,r} = Ḣ(t)·r. The Poincaré-disk area (Γ_0 − 1)·2π of the same circle is the galactic geodetic precession angle per orbit, the structural counterpart of the de Sitter—Fokker precession, but suppressed by v_∞²/2c² ~ 10u207bu2076 throughout cosmic history.In galactic cores the same isorapidity circle enters the strong-field regime. The exact geodetic precession angle per orbit of the accretion disk is given by [(1−α)(1−α/2)]^(−1/2) − 1, multiplied by 2π, where α = r_s/r, and is parameter-free beyond M and r/r_s. This yields five falsifiable predictions requiring no black-hole spin: (1) a universal ISCO frequency ratio ν_G/ν_orb = 0.374, independent of mass; (2) a jet precession period of approximately 26 years for M87* at r = 10·r_s, testable with VLBI monitoring; (3) a low-frequency QPO floor in low-spin systems at the predicted geodetic ratio; (4) a distinct radial QPO frequency profile discriminable from nodal and periastron precession across a state transition; and (5) a spinless disk warp with a radial profile distinct from the Bardeen—Petterson shape.
Category: Astrophysics
[1608] ai.viXra.org:2606.0066 [pdf] submitted on 2026-06-26 20:18:45
Authors: J. W. McGreevy
Comments: 14 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a complete first-principles derivation of the Standard Model gauge groupSU(3)c × SU(2)L × U(1)Y with three chiral generations of fermions, hierarchical masses,CKM/PMNSmixing, theseesaw mechanism for neutrinos, and Einstein—Cartan gravity withtorsion from one arithmetic object. The underlying structure is the resonant spectral tripleof the Bost—Connes system deformed by shear terms sourced by the class-group torsion ofirregular primes. In the deep infrared, the Chamseddine—Connes spectral action is evaluatedunder the global constraint of weight-12 principalization at the mirror point s = 6 of theassociated L-function.The fundamental duality between analytic volume (hyperbolic geometry, spectral flow,Seeley—DeWitt expansion) and algebraic rigidity (stabilizer symmetries at the two complexmultiplication points, adelic closure, weight-12 condition) is resolved by the irregular-primeshear, generating the pressure gradient ∇P that drives all symmetry breaking and massgeneration. Gauge representations emerge from the 3-cycle at τ = ρ and 4-cycle at τ = i;the bifundamental field Φ acquires a dynamical VEV; the 12×12 mass matrix, includinga natural seesaw for neutrinos, follows from breathing corrections sourced by class-grouptorsion. Numerical diagonalization over the full table of 47 irregular primes yields hierarchical fermion masses, realistic mixing, and a non-zero Jarlskog invariant. Confinement, thepositive mass gap, emergent proper time as a lapse function, and the Born rule all followfrom the same infrared thermodynamics.This construction realizes a complete arithmetic unification in which every low-energystructure is forced by the irreducible duality between analytic volume and algebraic rigidityunder weight-12 principalization. No external parameters beyond the shear amplitudes ofthe irregular primes are required.
Category: Mathematical Physics
[1607] ai.viXra.org:2606.0065 [pdf] submitted on 2026-06-25 19:21:40
Authors: Kesan Yi
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
If it is declared that real numbers are countable, the Cantor's diagonal process must be discussed. We try to find the problem of Cantor's proof by using the same method and logic to prove that a countable set is uncountable. That means real numbers may be a countable set but it was proved uncountable by Cantor's diagonal process. By critically analyzing the ontological foundations of the "Abstraction of Actual Infinity", we expose an illicit methodological shift in classical set theory: the unrestricted extension of actual infinity from the internal generation of infinite sets to external mappings between distinct infinite totalities. By redefining countable infinity purely through an intrinsic single-valued successor operations derived from the Peano framework, we bypass the mapping dilemmas of Cantor's definition of countable set with abstraction of actual infinity. Utilizing this new framework, we construct a "Right-ward Mirroring Successor Operator" capable of sequentially traversing all decimal expansions of real numbers within the interval [0, 1), thereby establishing that real numbers are countable under both potential and actual perspectives of infinity. Finally, we expose a fatal logical rupture within the Dedekind cut framework regarding the synchronization of measure theory derived from uncountable reals and total order set, validating our countable thesis as a necessary resolution to the internal contradictions of classical continuum mechanics.
Category: General Mathematics
[1606] ai.viXra.org:2606.0064 [pdf] submitted on 2026-06-25 10:42:25
Authors: Ginanjar Utama
Comments: 10 Pages.
Loop quantum gravity (LQG) is usually formulated as a quantisation of geometry, while operational measurements of length, time, and orientation are made through relations among matter fields. Penrose’s combinatorial spacetime and Altaisky’s recent locally Lorentzian matter-spin-network construction suggest a matter-first route: interaction events form the vertices of a graph, fermion-line segments form its edges, and geometry is reconstructed from the relations carried by those lines. We develop this kinematical proposal into an induced dynamical model with a computable discrete field equation. In the spacetime algebra Cl(1, 3), the SL(2, C) interaction vertices become versors; their sandwich action transports the matter-built tetrad, agrees with both the Hermitian-matrix and Ruehl Lorentz maps, and sends elementary areas to simple grade-two blades. Loop curvature is the bivector logarithm of a holonomy and is classified by the scalar and pseudoscalar invariants of B2; the generic loxodromic case is handled by a closed-form commuting elliptic—hyperbolic split. Because the discrete Grassmann matter action is bilinear, its path integral is the exact fermion determinant Z = det D. On an oriented graph Dirac operator, gauge invariance reduces Z to a functional of cycle-space holonomies, whileloops that share interaction events fail to factorise. The connected non-factorising determinant defines the interaction part of the effective action. Varying Seff = − log | det D| gives a local, gauge-covariant stationarity condition relating each independent cycle connection to the fermion propagator. Flat geometry solves the homogeneous equation as a Lorentzian saddle, and fixed boundary holonomies source curvature in the remaining cycles. We demonstrate the construction on the tetrahedral S^2 toy universe and on the K5 four-simplex 1-skeleton. The resulting equation is induced, Sakharov-style, and no continuum limit to Einstein gravity is claimed.
Category: Quantum Gravity and String Theory
[1605] ai.viXra.org:2606.0063 [pdf] submitted on 2026-06-24 06:05:24
Authors: Jason Merwin
Comments: 16 Pages. link is provided to the GitHub repository
We report the emergence of a finite carrier vacuum and macroscopic collision-fracture dynamics within a Distinction Combinatorial, a discrete relational growth model. We demonstrate that the reduced boundary grammar natively forms a hard-core carrier sea (measured densityρC ≃ 0.019092) that organizes into paired capsules, produces nilpotent defect-repair cascades, and supports coherent two-phase carrier-current propagation. This supplies a structured discrete medium, establishing that particle-like bridge formation propagates through a finite capsule sea capable of retaining route memory and observable topological scars.When driven to extreme local density, this discrete vacuum exhibits a deterministic transition. Anchored by the E24 energy tier—which naturally produces a symmetric topological fracture quantitatively aligning with the kinematics of the CMS CMS 6.14 TeV wide-dijet display—we analyze the primary E30 collision channel. The E30 channel reaches a strict bridge peak of $15C_{m AB}$ and shatters via 15CAB → 8CA + 7CB + 15Cspent. Route-flow analysis reveals the underlying graph-mechanical law governing this high-energy scattering: a finite zero-anchor capacity funnel. Contact selections virtually reroute capacity by creating transient replacements, which feeder selections sequentially actualize and consume. As the local zero-anchor pool drains linearly from 15 to 0, the available interaction space collapses, forcing a deterministic final fracture at edge 78--1549. The post-fracture debris retains distinct topological scars (an upstream B-side route-memory hub and a final edge-fracture scar), demonstrating that high-energy path dependence is not a stochastic failure of a continuum, but the execution of remaining legal graph moves within a depleted discrete vacuum.Finally, we project this microscopic vacuum structure to the cosmological scale. The raw finite-count de Sitter baseline is 5.27% high relative to a flat ΛCDM comparison. By applying the open-to-mature registry factor (124/120) and the natively measured microscopic carrier density (1 + ρC ), we derive a combined multiplier of 1.05306, seamlessly closing the residual to match the required 1.05272. This unified result links the local topological density of the discrete foam directly to the global cosmological constant.
Category: High Energy Particle Physics
[1604] ai.viXra.org:2606.0062 [pdf] submitted on 2026-06-24 02:55:22
Authors: J. W. McGreevy
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a complete analytic derivation of color confinement and a positive Yang—Millsmass gap within the Relativistic Field Theory of Primes (RFTP). The derivation is carriedout on a shear-deformed resonant spectral triple constructed from the Bost—Connes systemand its low-temperature KMS states. Irregular primes deform the underlying GNS quadraticform, generating a pressure gradient between the two complex-multiplication points τ = ρand τ = i on the modular curve. A continuous infrared renormalization-group flow thenproduces an infrared dichotomy: states whose phase lies outside the weight-12 lattice acquirean infinite entropy barrier (leading to confinement), while color-singlet states remain stable with a strictly positive mass gap controlled by the dominant shear amplitude.The proof relies on the asymptotic behavior of the heat kernel on the full GNS Hilbertspace, an effective Hamilton—Jacobi dynamics in which the arithmetic pressure gradient acts as the driving force, and the thermodynamic interpretation of the infrared divergenceas the failure of an arithmetic Legendre transform (principalization) for fractional-phase states. Both confinement (via the Wilson-loop area law) and the mass gap are shown toemerge directly from the infrared structure of a single spectral object without additionalassumptions or fine-tuning. The dynamical vacuum expectation value that will generatefermion masses in extensions of this framework is recovered as the equilibrium of the samedriven dynamics. This work establishes that color confinement and the mass gap are not accidental features of non-abelian gauge theories but inevitable consequences of the arithmetic geometry of the primes when viewed through the lens of a resonant spectral triple.
Category: Mathematical Physics
[1603] ai.viXra.org:2606.0061 [pdf] submitted on 2026-06-22 19:48:26
Authors: Michael Zot
Comments: 19 pages; English; formal continuation of ai.vixra 2606.0038.
Public mental-health education helps people name harmful behavior, seek support, and leave abusive dynamics. This paper does not argue against public education. It identifies an adversarial failure mode in open-audience psychological communication: the same detection rules that help victims and bystanders identify harm can also teach motivated actors what to stop showing.The proposed framework identifies Detection-Rule Leakage, the process by which public abuse-detection rules, clinical vocabulary, and relational safety scripts become visible to the same actors those rules are meant to expose. Once detection rules become public, an actor can update presentation style by replacing overt hostility with approved psychological language. This upgraded presentation is called Trust Camouflage.The paper’s central safeguard is function over form. It does not ask observers to memorize suspicious phrases. It asks whether language preserves repair, evidence, accountability, proportional consequences, and pattern visibility over time. The manuscript presents a falsifiable cognitive-security framework, a pre-validation coding protocol, testable hypotheses, and a validation roadmap. It is not a diagnostic, clinical, legal, custody, HR, or relationship-verdict tool.
Category: Mind Science
[1602] ai.viXra.org:2606.0060 [pdf] submitted on 2026-06-23 20:56:31
Authors: Javier Hidalgo Fernández
Comments: (Note by ai.viXra.org Admin: Please cite listed scientific references) 13 figures, and 28 tables. AI assistance was used for academic language polishing throughout the manuscript, Python code development, and cover page creative elements.
This work presents a detailed study on projectile motion when two marbles meet at their maximum height. I observed that the classic formulas in textbooks, as well as those found on web pages, do not mention the exceptional case of the moment when two marbles coincide in the air at their maximum height. Through an experimental analysis documented by high-precision videography and the use of integral and differential calculus tools, I was able to observe this finding, through the use of GraviTrax for kinematic experiments which, when combined with the rigor of physics and mathematics, has enormous educational value. After a persistent effort and careful preparation using complex formulas, I reinforced my hypothesis after observing the videos. The frames per second at the moment of collision are evidence that the velocity of each marble increases as a force is created at that point, attracting both marbles. As an independent researcher, I present this ansatz to the scientific community, demonstrating that the proposed formula accurately predicts the behavior of the marbles at that moment. Consequently, the validity of this study depends on monitoring the marbles' temperature at that moment. As demonstrated in the Methods section, the absence of temperature variation confirms the thermal stability necessary to validate the model.
Category: Classical Physics
[1601] ai.viXra.org:2606.0059 [pdf] submitted on 2026-06-23 23:09:24
Authors: Rüdiger Giesel
Comments: 43 Pages.
We formulate a compact effective-field-theory version of an octonionic projection model for the origin and calibration of fundamental constants. The model treats the constants not as isolated inputs, but as effective quantitiesarising from emergent spacetime projection, quantum phase normalization, and dynamical vacuum selection inside the non-associative octonion algebra. The non-associative sector is governed by an octonionic field triplet and itsassociator energy. Within this framework, the speed of light is interpreted as the conversion between projected time and space units, the quantum of action as the conversion between action normalization and quantum phase, Newton’sconstant as the inverse stiffness of the projected vacuum, and the cosmological constant as residual vacuum curvature. Gauge couplings are represented as eigenvalues of a vacuum-dependent kinetic tensor rather than fixed bare group numbers. An explicit Fano-plane calculation supplies algebraic normalizationreferences and shows why a strongly non-associative vacuum would generate a Planck-scale curvature contribution, whereas the observed smallness of the cosmological constant requires a nearly associative physical vacuum. Thereport provides a numerical-closure step based on a controlled one-parameter vacuum deformation and an exact calibration condition for Newton’s constant. It does not claim that all observed constants follow from the Fano plane alone;instead, it identifies the vacuum, projection, spectral and renormalization data required for parameter-free prediction.
Category: Relativity and Cosmology
[1600] ai.viXra.org:2606.0058 [pdf] submitted on 2026-06-22 01:34:15
Authors: James R. Johnson
Comments: 21 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The Fermi paradox asks why evidence of extraterrestrial Intelligent Civilizations (IC) with the ability to communicate has not been observed if the galaxy is abundant with habitable planets. A four-step quantitative framework was developed that incorporates pre-biological (galactic/star/planetary), biological, temporal, and detection bottlenecks. The first step estimates conditional probabilities for: the Galactic Habitability Zone (GHZ), pre-planet stellar environment, long-term planetary HZ, planet habitability, and long-term climate/chemistry. The result was ~58,000 habitable planets in the Milky Way galaxy over cosmic history. Step two applies Carter’s hard-steps model to estimate the probability (P) of intelligent life emerging within a ~5 Gyr habitable window. By adopting seven evolutionary steps with characteristic timescale of 1 Gyr, the model yields P ~ 0.095. Thus, ~5,500 IC existed in the Milky Way over cosmic time. Step three incorporates temporal overlap using a civilization lifetime of 10,000 years and an effective galactic lifetime of 5 billion years, reducing the expected number of contemporary IC to ~0.011 or effectively zero. Step four calculates radio detection limits based on a 12,000 Lyr radius, restricting detection to 6% of the galaxy. Thus, the absence of confirmed radio contact is consistent with the combined effects of habitability constraints, IC evolutionary timescales, temporal non-overlap, and detection limits. This is true even when significantly more optimistic assumptions prevail. Under this framework, the lack of observed signals does not constitute a paradox but rather an expected outcome.Keywords: Intelligent Civilization (IC), Biological bottlenecks, Non-biological bottlenecks, Exoplanets, Fermi Paradox, Drake equation, Carter equation, Milky Way, Radio detection constraints, Temporal overlap, Technosignatures, Habitability Zone (HZ)
Category: Astrophysics
[1599] ai.viXra.org:2606.0057 [pdf] submitted on 2026-06-22 04:30:28
Authors: Pruk Ninsook
Comments: 40 Pages.
This paper presents a zero-parameter consequence for the fine-structure constant (α) from the topological and information-geometric properties of a single Oloid manifold, under one explicitly stated physical postulate.Within the Information-Geometric Phase-Structure (IGPS) framework, we introduce the Distinguishability Coupling Principle: the postulate that the strength of the electromagnetic interaction is the operational distinguishability of the coupled charge sectors. Rather than positing the metric, we show that the Fisher—Rao form, the Bures metric, and the linear (length) accumulation are consequences of this principle — via the Chentsov—Petz classification (given a charge-preserving coarse-graining assumption), quantum measurement theory (Cramér—Rao bound), and the scale-freeness of the gapless seam CFT.Key Findings:The closed-form result: The geometric tree-level value and a self-consistent one-loop (Dyson) correction give:1/α = 8√3π² + (12 + 1/2π)πα ≈ 137.036The principal evidence is the tree term, which reproduces 1/α to 0.2% with no inputs; because it supplies 99.8% of the total, the geometry-fixed stiffness sits on a knife edge (correct to ~0.02%). The full relation matches CODATA to 3 × 10u207bu2076, though this figure is a low-sensitivity test of the correction coefficient rather than a high-precision one.No-Go Theorem for the quadratic count: In a scale-free 2D free-boson CFT (c=1), a dimensionless distinguishability count must be a Riemannian length (linear in the field), definitively excluding the energetic/quadratic (237) reading.Two-loop exactness: The O(α²) correction vanishes identically via the Schwinger-model exactness of the vacuum polarization, so no higher-order truncation is dropped.Structural by-products: The framework relates the Standard Model's colour and generation multiplicities (Nc = Ngen = 3) to one Z3 of the trefoil seam, via the Alexander polynomial — modulo one flagged Standard-Model-to-seam identification.Epistemic Status:We carefully separate what is rigorously derived from what remains a stated geometric primitive (the Fisher root √F = √3π and the discretization scale enter as primitives, not derivations). Every numerical ingredient — the phase area (8π), the contact-line modulus (√3), the WZW vertex (12), and the APS index term (1/2π) — is established independently in earlier IGPS papers without tuning against α. The tree-level weak mixing angle sin²(θ_W) = 1/4 lands 8% from experiment and is flagged as open. The framework's absolute mass scales remain open, requiring one external dimensionful anchor (akin to Λ_QCD and v in the Standard Model).
Category: High Energy Particle Physics
[1598] ai.viXra.org:2606.0056 [pdf] submitted on 2026-06-22 11:57:58
Authors: E.P.J. de Haas
Comments: 57 Pages. https://doi.org/10.5281/zenodo.20796685
Flat galactic rotation curves and the Baryonic Tully-Fisher relation have resisted explanation for five decades. Dark matter and modified gravity each resolve the problem by importing something external — either undetected matter or a modified law. A third route exists.A preceding empirical programme showed that the condition that total kinetic energy is conserved along galactic streamlines — the constant-Lagrangian (CL) condition — fits 175 observed rotation curves using only two physically meaningful parameters, the bulge radius and enclosed mass, without dark matter. That condition was a postulate. This paper derives it.Starting from a single first-order field equation for the gravitational vacuum flow, a channel decomposition automatically produces Newtonian gravity, the FRW expansion scalar, and the disk's rotation curve as three independent projections. The CL condition emerges as an exact internal output of the norm channel. Flat rotation curves, the Tully-Fisher scaling, and the cosmological structure of galactic disks follow simultaneously, with no free parameters.
Category: Astrophysics
[1597] ai.viXra.org:2606.0055 [pdf] submitted on 2026-06-22 18:38:02
Authors: Nigel B. Cook
Comments: 5 Pages.
We present a unified analytic framework in which weak-interaction radioactive decay and neutrino flavour oscillations arise as two branches of a single exponential—oscillatory duality. The key mathematical observation is that multiplying by i in the exponent converts oscillatory behaviour into exponential damping.
Category: Quantum Gravity and String Theory
[1596] ai.viXra.org:2606.0054 [pdf] submitted on 2026-06-21 00:47:37
Authors: Nigel B. Cook
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite and listed scientific references!)
We use Euler's formula to replace exp(iX) with cos X, and simply use Euclidean spacetime for quantum field theory and quantum mechanics; a "real" electron is an uncancelled resultant amplitude. This paper has been AI peer-reviewed checked, for mathematical typesetting accuracy, due to the total lack of interest of other humans in this topic!
Category: Quantum Physics
[1595] ai.viXra.org:2606.0053 [pdf] submitted on 2026-06-21 00:39:11
Authors: Allan Plankhart
Comments: 3 Pages. (Note by ai.viXra.org Admin: Part of the diagram is cut off)
We present a timeless mathematical construction of a pre-Big Bang universe. Starting from theempty set, we generate an infinite alternating chain of "something" and "anti-something", buildhigher-dimensional arrays, collapse to dimensions 1—3 due to Hurwitz’s theorem, introduce complex-valued fields with a U(1) symmetry ("oscillations" without time), ascend the division algebra ladderC → H → O, recover the Standard Model gauge group via Cohl Furey’s functor, extract electro-magnetic and spinor fields, and finally let time emerge as a monoid action R≥0 on the field space.The entire pre-temporal phase is a static diagram of functors and natural transformations; no timeparameter appears until the last step.
Category: Mathematical Physics
[1594] ai.viXra.org:2606.0052 [pdf] submitted on 2026-06-20 03:30:59
Authors: Sayo Asanagi
Comments: 28 Pages.
The upper tail of the individual wealth distribution in human societies universallyfollows a power law P (w) ∝ w−κ with Pareto exponent κ ∈ (1.5, 2.5), yet a fullyendogenous derivation of κ from economic first principles has remained an open prob-lem. We introduce the Arbitrage-Driven Wealth Distribution (ADWD) framework,founded on four base axioms (rationality, wealth-proportional information access,time-scale separation, and finite arbitrage lifetime) and three developmental axioms(determination of trading time, arbitrage arrival rate, and lifetime—trading-time con-sistency). From these axioms alone we derive a Fokker—Planck equation governingthe evolution of the wealth density P (w, t) with fully endogenous drift and diffusioncoefficients. The stationary solution yields a Pareto distribution whose exponent isgiven byκ = 1 + 2μlossαδ0,where every parameter carries a precise economic meaning. The dissipation rate μlossis decomposed without additional axioms into three components: consumption dis-sipation μC = ρ (from the rationality axiom via Ramsey optimisation), depreciationdissipation μD = 1/γ (from the finite lifetime axiom), and equilibration dissipationμE = αW 2∞/(N δ0) (from the information-access and time-scale axioms). The ag-gregate wealth ceiling W∞ emerges endogenously from a logistic structure implicitin the axioms, satisfying a self-consistency equation. A growth-correction term (theβ-term) is derived in three stages: a dynamic extension of the information-accessaxiom, a Nash equilibrium argument that identifies β = (1 − κ)β1/2, and a pertur-bative verification showing that the β-term vanishes at stationarity while governingthe transient approach to the power law. We establish two bridging theorems. The-orem P shows that Piketty’s qualitative criterion r > g is a special case of ourframework, recovered in the limit μD, μE → 0, and is sharpened to the quantita-tive condition αηW∞ > μloss. A correspondence theorem identifies the Bouchaud—Mézard exchange model as the limiting case ρ → 0, γ → ∞ of ADWD, providingthe economic micro-foundation that the physical model lacks. Finally, we proposea three-equation empirical protocol for estimating the sole non-directly-observableparameter α from wealth-distribution data, transaction frequencies, and aggregategrowth rates, enabling in-principle falsification of the theory
Category: Economics and Finance
[1593] ai.viXra.org:2606.0051 [pdf] submitted on 2026-06-19 11:33:11
Authors: Nick Markov
Comments: 19 Pages.
Gravity is traditionally described through the curvature of spacetime or, in the Newtonian limit, through the gravitational potential generated by mass. In this work, we explore the possibility that gravitational phenomena may be interpreted as manifestations of cumulative relativistic interaction delays associated with finite-speed propagation within self-gravitating systems. Rather than modifying established gravitational laws, the approach seeks to provide a causal interpretation of gravitational potential and spacetime curvature in terms of accumulated propagation delays between source and observer.The proposed interpretation is examined across three distinct astrophysical regimes. First, self-gravitating planetary and stellar bodies are considered. The framework implies a connection between characteristic internal propagation speeds and escape velocities through the equivalence of the associated relativistic time-dilation factors. Comparison with observational data reveals a close correspondence between these quantities in gravity-shaped bodies possessing coherent internal propagation paths.Second, the framework is extended to galaxies, where gravitational and kinematic time-dilation effects coexist. In this mixed regime, orbital motion contributes significantly to the cumulative delay, providing a natural interpretation of the observed connection between characteristic velocities and gravitational dynamics.Third, galaxy clusters are examined as systems in which collective kinematic effects become increasingly important relative to gravitational time-dilation contributions. Observed relations among velocity dispersion, gravitational redshift, and lensing mass are shown to be consistent with the hypothesis that these observables probe a common underlying delay structure. In this interpretation, planetary interiors, galaxies, and galaxy clusters probe cumulative interaction delays through internal material propagation, mixed material—gravitational interactions, and large-scale gravitational dynamics, respectively.The results suggest that cumulative relativistic interaction delay provides a unified phenomenological interpretation of gravitational behavior across multiple astrophysical scales. The proposed framework preserves the observed gravitational phenomenology described by General Relativity while offering a possible physical explanation for the origin of the associated spacetime curvature. This interpretation motivates further investigation of finite-speed interaction effects in self-gravitating systems.
Category: Relativity and Cosmology
[1592] ai.viXra.org:2606.0049 [pdf] submitted on 2026-06-18 08:22:43
Authors: Hacı Soğukpınar
Comments: 59 Pages.
Neutrino oscillations represent one of the most important discoveries in modern particle physics and provide direct evidence that neutrinos possess non-zero masses and undergo flavor transformations during propagation. Within the Standard Model framework, neutrino oscillations are described through the Pontecorvo—Maki—Nakagawa—Sakata (PMNS) mixing matrix, which relates flavor eigenstates to mass eigenstates. Although this formalism successfully explains solar, atmospheric, reactor, and accelerator neutrino experiments, the fundamental origin of neutrino masses, flavor mixing, and oscillation dynamics remains an open question. The existence of neutrino oscillations therefore points toward physics beyond the original Standard Model. Unified Fractal Quantum Field Theory (UFQFT) proposes an alternative interpretation in which neutrinos are not fundamental particles but stable resonance configurations emerging from coupled energy (Φ) and charge (Ψ) fields embedded within a critical fractal spacetime characterized by an effective dimension near (D= 2.7). In this framework, neutrino oscillations arise from resonance mixing, geometric overlap between resonance states, and fractal phase evolution during propagation. Flavor transitions are interpreted as resonance transformations rather than oscillations between fundamental mass eigenstates. In this work, a comprehensive UFQFT description of neutrino oscillations is developed and compared with the conventional PMNS formalism. A resonance-mixing framework is introduced to describe electron-, muon-, and tau-neutrino transformations, and oscillation probabilities are derived from geometric resonance overlap and phase evolution in fractal spacetime. The model is applied to solar neutrino observations, atmospheric neutrino measurements, reactor experiments, and long-baseline accelerator studies. Particular attention is given to the experimental programs of DUNE and Hyper-Kamiokande, which provide powerful opportunities for testing resonance-based predictions. The analysis investigates whether the observed neutrino oscillation phenomenology can emerge naturally from resonance dynamics while preserving agreement with current experimental data. The results suggest that neutrino flavor transitions may be interpreted as manifestations of resonance geometry and fractal phase evolution, providing a unified framework connecting particle mixing, spacetime structure, and resonance dynamics. This study constitutes a key component of the UFQFT Standard Model Validation Program and establishes the theoretical foundation for future investigations of leptonic CP violation, matter—antimatter asymmetry, and the role of neutrinos in cosmology.
Category: High Energy Particle Physics
[1591] ai.viXra.org:2606.0048 [pdf] submitted on 2026-06-18 10:18:25
Authors: Nick Markov
Comments: 10 Pages.
Escape velocity and internal propagation speed are generally regarded as independent properties of self-gravitating bodies. Escape velocity is determined by the global gravitational potential, whereas propagation speed depends primarily on local material properties such as density and elastic response. Here we report a previously unrecognized correspondence between these quantities across a range of gravity-shaped bodies. Observational data for Earth, Mars, Venus, the Moon, and the Sun indicate that characteristic internal propagation velocities closely match the corresponding escape velocities despite substantial differences in composition, thermodynamic state, and evolutionary history.The observed relation spans more than two orders of magnitude in characteristic velocity and appears to hold for both planetary and stellar interiors. For tidally locked bodies such as the Moon, a geometric correction associated with non-radial propagation yields the same scaling behavior. The correspondence is quantified through the dimensionless ratio �� = �� ��������/�� ��, which remains close to unity across the investigated bodies within observational uncertainty.The relation was originally identified as a consequence of a broader framework in which gravitational potential is associated with cumulative relativistic interaction delay. Within that framework, equating the relativistic time-dilation factors associated with finite-speed propagation and gravitational potential leads directly to the observed scaling. Although the physical origin of the correspondence remains open, the results suggest an unexpected connection between internal propagation processes and gravitational potential. Future planetary, lunar, and helioseismic observations may provide additional tests of the proposed relation.
Category: Relativity and Cosmology
[1590] ai.viXra.org:2606.0047 [pdf] submitted on 2026-06-19 03:26:58
Authors: E. P. J. de Haas
Comments: 144 Pages. https://doi.org/10.5281/zenodo.20747973
The biquaternion (BQ) algebra, realized at the Pauli-spin level as the full matrix algebra (M(2,mathbb{C})), provides a compact framework in which classical field theories can be organized through a common hierarchy of algebraic products and channel decompositions. This paper develops that hierarchy for both electrodynamics and relativistic fluid dynamics and explores the structural relationships that emerge between them.In electrodynamics, the BQ hierarchy reproduces the electromagnetic field, Lorentz force law, Maxwell equations, wave equations, and interaction-conservation relations from a sequence of algebraic products involving the four-current and four-potential. In relativistic fluid dynamics, the corresponding hierarchy generates the continuity equation, Bernoulli relation, vorticity transport, Euler—Lamb momentum balance, acoustic wave equations, helicity relations, and stress-energy conservation through analogous products of the fluid four-velocity and momentum-density field.The central result is that both theories share the same four-level algebraic structure and the same geometric channel decomposition. The force equations (JB=F) and (UH=F) emerge as the unique four-channel level of their respective hierarchies, revealing a common organization that is largely hidden in conventional formulations. The analysis further identifies the acoustic refractive index (n_s=c/c_s) as a hierarchy-wide parameter linking relativistic and practical fluid dynamics, and locates the greater complexity of fluid dynamics in the self-referential coupling between velocity and momentum-density fields.The paper does not introduce new physical postulates. Rather, it proposes that the BQ channel decomposition provides a unified organizational framework that makes structural relationships between electrodynamics and fluid dynamics explicit, offering a common language for force, energy, momentum, vorticity, helicity, and wave phenomena across both theories. In this sense, the work is intended as a conceptual and educational framework as much as a mathematical formalism, and as a foundation for future applications in gravitation, magnetohydrodynamics, and AI-assisted symbolic physics.
Category: Mathematical Physics
[1589] ai.viXra.org:2606.0046 [pdf] submitted on 2026-06-19 03:25:24
Authors: Fernando Salmon Iza
Comments: 4 Pages.
For decades, the scientific community has recognized that our universe is expanding at an accelerating rate (Riess A. G. et al., 1998); however, in some respects, cosmology has not taken this into account. The FLRW metric assumes that time has always passed in the same way at every moment and place, that is, that the Lapse function is equal to one. In recent years, this problem has been studied in greater depth (Melia, F., 2019, 2023), demonstrating that a Lapse function equal to one is only valid for non-accelerating universes and not for accelerating ones. Therefore, errors are made when referencing times to reference frames with a Lapse function equal to one, so these times are not the true times. It is necessary to find an inertial reference frame in our accelerating universe that allows us to determine times correctly, and to find it, we must modify the Lapse function. In this work, we have studied what the Lapse function should be in order to lead to a free-fall reference frame and in it determine the true times of the ages of galaxies.
Category: Relativity and Cosmology
[1588] ai.viXra.org:2606.0045 [pdf] submitted on 2026-06-18 03:30:30
Authors: Hacı Soğukpınar
Comments: 40 Pages. (Note by ai.viXra.org Admin: Further repetition may not be accepted)
Weak interactions constitute one of the four fundamental interactions of nature and play a central role in particle transformations, beta decay, neutrino physics, and flavor-changing processes. Within the Standard Model, weak interactions are described by the electroweak gauge theory based on the symmetry group SU(2)u2097 × U(1)ᵧ and are mediated by the massive W and Z bosons. Although this framework has achieved remarkable experimental success, several fundamental questions remain unresolved, including the physical origin of flavor transitions, the nature of weak bosons, the origin of mixing matrices, and the connection between weak interactions and the underlying structure of spacetime. Unified Fractal Quantum Field Theory (UFQFT) proposes an alternative interpretation in which weak interactions emerge from resonance transformations occurring within coupled energy (Φ) and charge (Ψ) fields embedded in a critical fractal spacetime characterized by an effective dimension near D ≈ 2.7. In this framework, particles are not regarded as fundamental objects but as stable resonance configurations, and weak processes correspond to transitions between resonance states. The transformation of up and down quark resonances, beta decay, flavor mixing, and weak-boson phenomena are interpreted as manifestations of resonance evolution rather than fundamental gauge-mediated interactions. In this work, we develop a systematic formulation of weak interactions within UFQFT and compare it with the Standard Model description. The resonance transformation mechanism is applied to neutron beta decay, charged-current and neutral-current processes, flavor mixing, and weak decay phenomena. Theoretical predictions are compared with experimental observations including neutron lifetime measurements, weak decay rates, and precision electroweak data. We further investigate whether the effective gauge structure of the Standard Model may emerge as a low-energy approximation of a deeper resonance-geometric framework. The results suggest that weak interactions can be consistently interpreted as resonance transformations while preserving the observed conservation laws and phenomenological behavior of known weak processes. This study represents a key component of the UFQFT Standard Model Validation Program and provides a foundation for subsequent investigations of neutrino oscillations, CP violation, and matter—antimatter asymmetry within a unified resonance-based framework.
Category: High Energy Particle Physics
[1587] ai.viXra.org:2606.0044 [pdf] submitted on 2026-06-17 18:55:28
Authors: Vladimir S. Netchitailo
Comments: 11 Pages.
A concise record of successful predictions is often more persuasive than hundreds of pages of theoretical development because it directly addresses the central question every physicist asks: What did the model predict before the observational data became available? In this paper, we present several quantitative predictions made by the World—Universe Model (WUM) in 2013 [1,2] that were subsequently confirmed by observations and measurements. These prior predictions constitute one of the strongest arguments for the long-term scientific significance of WUM.The paper presents a self-consistent set of (Q)-dependent, time-varying values for the primary cosmological parameters of the World, including the Newtonian gravitational parameter (G), the Hubble parameter (H_0), the concentration of intergalactic plasma, the minimum photon energy, the temperature of the Microwave Background Radiation (MBR), and the peak temperature of the Far-Infrared Background Radiation (FIRB). The obtained set of values was recommended for consideration in the 2014 adjustment of the CODATA Recommended Values of the Fundamental Physical Constants.
Category: Relativity and Cosmology
[1586] ai.viXra.org:2606.0043 [pdf] submitted on 2026-06-18 03:27:04
Authors: Paul Robert Mesler
Comments: 26 Pages. (Note by ai.viXra.org Admin: Please cite and listed scientific references!)
We conducted an experiment to test if proper orbital angular acceleration of two rotating bodies within a three-body system due to proper linear acceleration of the system would cause the center of mass momentum of the system to increase as predicted by Euler’s first law? The result would be significant because the increase in momentum would be due to the reaction of spacetime itself on a body that is forced off its natural geodesic path due to proper linear acceleration and not due to physical, external contact forces. Thirty test trials were conducted where two spheres were constrained to travel around quarter-circle tracks. This caused centrifugal reactive forces on the inner walls of the curves, forcing the system to linearly accelerate. This proper acceleration induced an increase in the orbital angular speed of the spheres by spacetime itself due to the non-geodesic motion of the spheres. After 30 test trials the 1 mean value of known external friction impulses acting on the three-body system accounted for only ~ 8.2 per cent (standard deviation .037 and standard error .0068) of the increase in the final momentum of the system, leaving a ~ 91.8 per cent discrepancy. This result highly suggested that spacetime itself contributed ~ 91.8 per cent of the total external impulse on the system.
Category: Classical Physics
[1585] ai.viXra.org:2606.0042 [pdf] submitted on 2026-06-15 20:59:49
Authors: Brent Hartshorn
Comments: 6 Pages. https://github.com/brentharts/introspecter
We describe a small system that treats the question "what is a self?" not as a thesis tobe proved but as an inquiry to be staged : made visible, evolved in documented steps, andshared. The system is a single PDF that carries its own source code as embedded file streams;a short appendix bootstrap extracts and runs that code to produce the next iteration. Itscontent is written in a small domain-specific language (DSL) whose symbols are simultaneouslymathematical notation, philosophical relations, and executable program. Each operator rendersas typeset mathematics, generates a natural-language question, and compiles to Python. Ahuman-in-the-loop step takes an "oracle" — a person, or a language model the person consults— that proposes the next evolution; symbolic statements are compiled to a fixed, sandboxed setof builder calls, while optional fenced code blocks may extend the engine itself, gated by explicithuman confirmation. We document the full pipeline, the minimal seed, and a worked examplein which the document grows a new relational operator. We are deliberate about what theinstrument does and does not establish: because the document can be rewritten to ask anything,the apparent depth of any stage is supplied by whoever authored it. The system is therefore afaithful instrument for staging an inquiry into selfhood; it is not, and by construction cannotbe, a demonstration that a self has emerged. We argue this honest framing is the interestingone.
Category: Linguistics
[1584] ai.viXra.org:2606.0041 [pdf] submitted on 2026-06-16 20:39:51
Authors: Hongshu Zhu
Comments: 9 Pages. (Note by ai.viXra.org Admin: Author name is required in the article after article title; and please cite and list scientific references)
This comprehensive manuscript proposes a profound paradigm shift in theoretical physics, offering a unified geometric framework that bridges the genesis of the universe, the mechanics of elementary particles, and the horizon of applied aerospace engineering. Diverging from the traditional Big Bang singularity, this hypothesis posits that the universe originated from the spatiotemporal topological collapse of a fourth spatial dimension, leaving behind microscopic "black hole-white hole" dual rotating oscillators—the geometric and fluid essence of all elementaryparticles. Within this Topological Fluid framework, the four fundamental forces(gravity, electromagnetism, strong, and weak interactions) are unified seamlessly asdistinct manifestations of fluid dynamics, and the classical mass-energy equivalence(E = mc2) acquires a pure geometric derivation.Advancing into applied physics, we define the mechanism of Topological Phase Locking, whereby extreme high-frequency electromagnetic resonance aligns the spatial emissions of these microscopic dipoles. By integrating this mechanism with the Ginzburg-Landau theory of superconductivity to eliminate thermal topological friction, we introduce the Non-Minimal Topological Coupling Lagrangian. This novel field-theory formalism proves that electromagnetic resonance within a macroscopicquantum coherent state forces a renormalization of the effective gravitational constant (Gef f < 0). This directly derives the Gravitational Meissner Effect—the absolute expulsion of the background gravitational spatial flux. Ultimately, this manuscript delineates a rigorous, propellantless geometric pathway for macroscopic topological thrust, the elimination of inertial mass, and Faster-Than-Light (FTL)metric traversal, offering theoretical alignment with contemporary anomalous aerodynamic observations.
Category: Quantum Gravity and String Theory
[1583] ai.viXra.org:2606.0040 [pdf] submitted on 2026-06-16 20:34:28
Authors: J. W. McGreevy
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a first-principles derivation of 3+1-dimensional Lorentzian spacetime andEinstein—Cartan gravity from the arithmetic structure of the Bost—Connes C∗-dynamicalsystem. Starting from the primitive object (ABC,σt) and its KMS states, we construct ascale-invariant quadratic form on the idèle class space via the GNS inner product. Irregularprimes appear as topological defects through class-group shifts, inducing a shear in thequadratic form that maps canonically to a point τp ∈ H. For the resonant prime 691 this shear aligns with the hexagonal fixed point τ = ρ, where the Z/6Z stabilizer providestopological protection against adelic screening.The local 3-defect patch (primes 37, 59, 691) carries a non-abelian su(2) connection.Global adelic closure projects the three independent directions onto a single screened ray (time) while preserving the protected 3-dimensional spatial structure generated by the Eisenstein lattice at ρ. Explicit differentiation of the quadratic-form embedding with respect to the shear parameter yields the six generators of the Lorentz algebra so(1,3), with compact rotations locked at resonance and non-compact boosts arising from unbounded shear.The second-order Magnus expansion of parallel transport produces a residual torsion vector whose components are fixed by phase mismatches between the three incommensurate modular frequencies. Promoting the local Quantum Geometric Tensor metric on the 3-defect patch together with the screened ray yields a derived 4D Lorentzian geometry. On the resulting resonant spectral triple we evaluate the Chamseddine—Connes Spectral Action. Functional variation with respect to the emergent metric produces the Einstein—Cartan field equations, with the cosmological term fixed by the converged quadratic sum over the 47 irregular primes below 691 and the torsion source fixed by the linear sum. The next heat-kernel coefficienta4 generates quadratic gravity corrections that are parametrically suppressed by the samearithmetic factors, establishing ultraviolet safety. All physical structures—spacetime signature, Lorentz symmetry, torsion, and gravitational dynamics—emerge as necessary consequences of adelic consistency acting on the arithmetic defects of the Bost—Connes system. No external gravitational or field-theoretic ansatzis introduced.
Category: Mathematical Physics
[1582] ai.viXra.org:2606.0039 [pdf] submitted on 2026-06-16 20:42:45
Authors: Michael Zot
Comments: 19 Pages.
This paper presents a contradiction-based proof that Minimal Irreversible Predictive Updates (MIPU) and Maximal Anticipatory Patterns (MAP) are necessary structural bounds for any finite system capable of integrated learning and anticipation. We define learning as a change in future prediction, classification, action, or response caused by new information. Under this definition, a learning system cannot change nothing, and any real predictive change must contain some necessary update. If all unnecessary components are removed from that update, the remaining smallest integrated prediction-changing component is a MIPU. Therefore, denying MIPU while preserving learning produces contradiction.We then define anticipation as the use of present information to constrain possible future states. Anticipation cannot occur without pattern structure. If the pattern is too small, valid predictive information is excluded. If the pattern is too large, unsupported structure enters and coherence fails. The widest coherent anticipatory structure available to the system is therefore a MAP. Denying MAP while preserving anticipation also produces contradiction.Together, MIPU and MAP define a bounded corridor for intelligence: below MIPU, information fails to become learning; above justified MIPU, evidence becomes distortion; below MAP, the system misses valid structure; above MAP, the system invents structure. The result is a formal foundation for analyzing human cognition, artificial intelligence, multi-turn model failure, manipulation detection, and other predictive systems through lower and upper bounds of valid predictive change.
Category: Artificial Intelligence
[1581] ai.viXra.org:2606.0038 [pdf] submitted on 2026-06-14 20:38:47
Authors: Michael Zot
Comments: 11 Pages.
This paper introduces the Open-Audience Pseudo-Psychology Risk Model (OAPRM), a framework for analyzing the risks created when clinical, forensic, and therapeutic concepts are converted into viral public content. Mental-health content about narcissism, gaslighting, love bombing, coercive control, DARVO, red flags, and abuse detection is typically framed as victim education. This paper argues that such framing ignores the open-audience structure of algorithmic platforms. In public feeds, victims are not the only viewers. Confused observers, false accusers, reputation managers, manipulators, and abusive actors can all receive the same detection rules.The paper identifies detection-rule leakage as the central failure: when content teaches victims what to recognize, it can simultaneously teach adversarial viewers what to hide. This creates asymmetric benefit. Victims may gain language for harm, while harmful actors may gain operational knowledge about which behaviors trigger suspicion. The paper formalizes this process through the concepts of Trust Camouflage, Weak Disclosure, Resilient Disclosure, and MIPU/MAP formation. Trust Camouflage describes the use of therapeutic language, such as boundaries, healing, accountability, and emotional safety, to appear trustworthy while maintaining harmful control dynamics underneath.OAPRM proposes that viral pseudo-psychology content should be evaluated not only by accuracy, intent, or creator credentialing, but by audience composition, adversarial uptake, disclosure resilience, and downstream behavioral adaptation. The paper argues that public abuse-awareness content can unintentionally degrade its own detection value when the people being described learn the signs and adapt around them. It concludes by proposing resilient disclosure principles for mental-health education that can support victims without broadcasting evasion manuals to adversarial audiences.
Category: Mind Science
[1580] ai.viXra.org:2606.0037 [pdf] submitted on 2026-06-14 20:30:26
Authors: Kasun Thilina Fernando
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper presents an alternative interaction-based interpretation of the single-slit and double-slit experiments. It proposes that interference-like patterns arise from attractive and repulsive interactions between photons or electrons and electrons near slit boundaries, rather than from traditional wave-particle duality alone. The model suggests that these interactions modify particle trajectories and produce observable fringe patterns. A classical analogy and discussion of slit geometry are included to support the concept, encouraging further theoretical and experimental investigation into quantum interference phenomena.
Category: Quantum Physics
[1579] ai.viXra.org:2606.0036 [pdf] submitted on 2026-06-13 04:12:37
Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 17 Pages.
We develop a physics of cortical dynamics in which a microscopic quantum realm and a macroscopicclassical realm coexist and are coupled at the synapse. Following Beck and Eccles, thetrigger for synaptic exocytosis is treated as a genuine quantum event governed by the position—momentum uncertainty relation (Part I); its environmental decoherence is a measurement eventin the von Neumann sense [1], and the population of such events seeds the noise of a classicalstochastic neural field whose Martin—Siggia—Rose—Janssen—De Dominicis path integral organizescortical fluctuations through a single parameter, namely Brain's Planck Constant; so that partof the cortical noise descends from it. Measurement event and perceptual decision areunified as one first-passage construction (Part III). We estimate Brain's Planck Constant from cortical parameters,validate the first-passage law numerically, obtain a falsifiable kinetic-isotope and temperaturesignature in synaptic release, decision error rate, and reaction-time variability, and read thearchitecture as a quantum—classical hybrid computer. We then derive (Part IV) the corticalfluctuation spectrum from a fluctuation—dissipation relation and compare it to the 1/f powerof EEG/LFP; develop the stochastic thermodynamics of the neural field, giving the brain’s effectiveBoltzmann scale and the Landauer cost of the synaptic measurement; and map brainstates, criticality and neuronal avalanches, and predictive-coding precision onto modulation ofBrain's Planck Constant. The quantum realm is real but confined to the molecular trigger; the classical realm governscognition; all dualist interpretation is kept outside the physics.
Category: Quantum Physics
[1578] ai.viXra.org:2606.0035 [pdf] submitted on 2026-06-13 20:24:28
Authors: Dainis Zeps
Comments: 13 Pages. (Note by ai.viXra.org Admin: This submisison may not fall within the scope of ai.viXra.org and is sucject to removal)
This paper continues an earlier experiment in prompt-based political reasoning by askingwhether narrative-driven discussion can be partially replaced by an axiomatic sequence ofprompts. The point of departure is a deliberately strong initial prompt concerning Russia’s forced federalization and demilitarization, treated not as a conclusion to be debated but as a working axiom from which further prompts can be generated. The paper argues that conventional political discussion, whether human or AI-assisted, tends tobecome trapped in normative reformulations, objections, and rhetorical loops that obscure rather than clarify reality. In contrast, the proposed method seeks prompts that are increasingly descriptive rather than normative, so that they function as compact pictures of reality rather than as wish-expressive political narratives. Using the war in Ukraine and the contemporary Russian imperial system as a test case, the paper shows how an initial prompt can generate a sequence of further prompts describing military deadlock, imperial self-destruction, social degradation, and the internal human cost of the Russian system. Particular emphasis is placed on the claim that the first victims of an imperial order may be the people living within it, and that this perspective remains largely invisible instandard Western political discourse.The paper does not present a finished formal theory. Instead, it offers a first methodological step toward a prompt-based axiomatics in which political reasoning proceeds by making assumptions explicit, refining them through further prompts, and replacing language-modelled narrative patterns with existence-guided pictures of reality.
Category: Social Science
[1577] ai.viXra.org:2606.0034 [pdf] submitted on 2026-06-13 20:57:11
Authors: Karen Lines
Comments: 7 Pages. (Note by ai.viXra.org Admin: This submision is speculative and may not be within the scope of ai.viXa.org; please cite listed scientific references)
The nature of dark matter remains unknown. This paper proposes a geometric model: dark matter is a primordial, slowly evolving foam — a continuous, fractal scaffold that constitutes the skeleton of the universe. Ordinary matter does not clump under pressure but instead fills the voids of this foam without resistance. This filling process explains the observed cosmic web (JWST COSMOS-Web map, 2026) as a ghost trace of the underlying foam. The foam is not strictly timeless; it evolves on timescales far longer than the current age of the universe, making it effectively static over cosmic history. Time dilation emerges from matter's position within the foam, with limits that avoid singularities and respect causality. Gravitational waves propagate through the foam walls analogously to pressure waves through Earth's atmosphere (Hunga Tonga 2022). The model accounts for redshift asa cumulative path effect, for large-scale structure without dark energy, and for the "tree ring" appearance of the cosmic web. The Local Void — a 150—300 Mly underdense region adjacentto the Local Group — provides a nearby laboratory. Observational predictions include:a quantitative gradient in stellar age and metallicity across the Local Sheet (∆[Fe/H]∼0.1− 0.2 dex per 10 Mpc), gravitational wave echoes from foam walls, and small-scale CMBanisotropies matching a fractal pattern.
Category: Relativity and Cosmology
[1576] ai.viXra.org:2606.0033 [pdf] submitted on 2026-06-13 21:00:28
Authors: Karen Lines
Comments: 4 Pages. (Note by ai.viXra.org Admin: This submision is speculative and may not be within the scope of ai.viXa.org; please cite listed scientific references)
We present the Gradient Foam Framework, a unified perspective on systems where a slowly evolving scaffold (foam) creates potential gradients along which a filler flows without pressure. This principle appears across scales: perfect numbers (abundancy index), the cosmic web (dark matter filaments), second sound in super-fluids, DNA hydrogen bonding, human population dynamics, technology evolution,and the topology of odd integers. We show that the odd positive integers form a M¨obius strip (a nonorientable, onesided space) in which the abundancy index can approach 2 arbitrarily closely but never reach it. The smallest odd abundant number, 945, marks the first crossing above 2 and serves as a numerical witnessto the topological obstruction. We introduce memention — the warm, directional bridge between memory and intention — as a dynamical vector in the foam, and we relate the impossibility of odd perfect numbers to a de Sitterlike 'conclusionary horizon': the odd perfect number can only exist in nonstandard models beyond thelimits of provability. The paper synthesises number theory, topology, physics, andinformation theory into a coherent cosmological picture: the foam holds, the number 2 is the guardian of twosidedness, and the nonexistence of odd perfect numbers is a necessary condition for a stable, flowing universe.
Category: Relativity and Cosmology
[1575] ai.viXra.org:2606.0032 [pdf] submitted on 2026-06-12 05:04:33
Authors: Paul Robert Mesler
Comments: 19 Pages.
Euler’s first law requires that changes in the center of mass momentum of a system of bodies can only occur when external impulses act on a system. We report the results of an experiment where after 30 test trials the mean value of known external friction impulses acting on a threebody system accounted for only ~ 8.2 per cent (standard deviation .037 and standard error .0068) of the increase in the final momentum of the system, leaving a ~ 91.8 per cent discrepancy. The three-body system consisted of two spheres, constrained to roll around quarter-circle barriers attached to a third body. Since the spheres were constrained from following their natural straight-line geodesic paths in the metric of flat spacetime, centrifugal real forces emerged radially outward from the center of mass of the spheres, pushing on the inner walls of the curved barriers. This caused the system to accelerate, inducing torque inertial forces on the spheres which increased their orbital angular speed. This increase in speed accounted for the ~ 91.8 per cent impulse discrepancy of the experiment, and thus, when added to the friction impulse, accounted for the total impulse that caused the increase in the center of mass momentum of the system per Euler’s first law.
Category: Classical Physics
[1574] ai.viXra.org:2606.0031 [pdf] submitted on 2026-06-12 18:09:02
Authors: Pruk Ninsook
Comments: 42 Pages.
This manuscript presents Paper X of the Information-Geometric Physics System (IGPS) series, extending the framework to the electroweak sector. It explores an approach where the Standard Model Higgs doublet is modeled as a BPS domain wall within a five-dimensional SU(2)_L × U(1)_Y gauge theory. By analyzing the spectral geometry and conformal field theory (CFT) of the Higgs kink worldvolume, this paper attempts to derive fundamental electroweak observables structurally, without introducing additional free parameters.Key Concepts and Results:The Weinberg Angle (sin²θ_W): Building on Callan-Harvey anomaly inflow and topological charge quantization, the framework yields a tree-level value of sin²θ_W = 1/4. This mathematically preserves the gauge boson mass ratio m_Z/m_W = 2/√3 and the exact custodial symmetry parameter ρ = 1.The Electroweak Worldvolume: Utilizing the Goddard-Kent-Olive (GKO) coset construction, we propose an identification of the combined lepton-Higgs worldvolume with the 3-state Potts minimal model M(5,6) carrying a central charge c = 4/5.The Higgs Quartic Coupling (λ_H): Formulated through structural VOA data, specifically combining the primary conformal weight with the UV crossover scale derived from the Schwinger-Dyson equation. This geometric approach yields λ_H = 31/240 ≈ 0.12917, showing a close numerical agreement (-0.17% deviation) with the current experimental value. This result subsequently provides a conditional estimate for the Higgs vacuum expectation value of v ≈ 246.4 GeV.The Observer Necessity Principle: Discussed in the Appendix, this section aims to formalize the mapping of 4D physical couplings from 2D CFT boundary data. By applying the Cauchy functional equation and standard thermodynamic identities, we outline a structural rationale for selecting the specific derivation route presented in this study.Overall, this paper aims to provide a topological and algebraic perspective on the Standard Model's dimensionless electroweak couplings, suggesting that these foundational parameters might be understood as structural invariants of an underlying spectral geometry.
Category: High Energy Particle Physics
[1573] ai.viXra.org:2606.0030 [pdf] submitted on 2026-06-12 01:43:58
Authors: Karen Lines
Comments: 6 Pages.
We propose a new cosmological principle for the foundations of arithmetic: the Dark Foam Universe. In this framework, the number 2 acts as the stabilising symmetry of a quantum foam of vacua. Even perfect numbers are the allowed,coherent structures that respect this symmetry, while an odd perfect number is a forbidden architecture that would break the conclusionary horizon—a logical boundary analogous to the de Sitter horizon in spacetime. We demonstrate thatevery known attack on the odd perfect number problem fails in a way precisely analogous to the impossibility of observing beyond a cosmological horizon. Using the mathematical apparatus of de Sitter space, nonstandard models of arithmetic, and the limits of provability, we argue that an odd perfect number can only inhabit a de Sitterlike 'unreal' place where knowledge is fundamentally inaccessible, andthat its nonexistence in the standard model of arithmetic is a necessary stability condition for the mathematical universe. The paper formalises this vision and shows how the number 2 guards the boundary between the real and the unreal.
Category: Relativity and Cosmology
[1572] ai.viXra.org:2606.0029 [pdf] submitted on 2026-06-10 21:28:40
Authors: J. W. McGreevy
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a fully rigorous, self-contained analytic proof that the non-trivial zeros of the Riemann zeta function are precisely the globally stable skin modes of an inner-fluctuated Dirac—Zeta operator on the compactified modular curve X(1)∗. The proof proceeds entirely within the framework of unbounded operators on weighted Sobolev spaces, regularized Fredholm determinants on Hilbert—Schmidt ideals, the Riemann—Roch theorem, and a vanishing theorem for fractional states. The simple pole at s = 1 is interpreted as a topological point gap that triggers the NonHermitian Skin Effect. Spectral stability under discretization is established via uniform pseudospectrum control. The point-gap winding number is realized as the Fredholm index of the regularized resolvent. Riemann—Roch divisor constraints on meromorphic sections force the Generalized Brillouin Zone onto the critical line. A vanishing theorem shows that isolated fractional (non-color-singlet) states are excluded from the domain, thereby locking every non-trivial zero to R(s) = 1/2. The construction is compatible with Alain Connes’ spectral triples and yields, as a byproduct, an explicit derivation of the Clausius relation from the spectral action along the adiabatic paths of the modular loop. All steps are topological and independent of any particular representative of the operator.
Category: Mathematical Physics
[1571] ai.viXra.org:2606.0028 [pdf] submitted on 2026-06-10 20:43:11
Authors: Vladimir S. Netchitailo
Comments: 6 Pages. (Note by ai.viXra.org Admin: Further repetition will not be accepted)
This paper summarizes key results of Classical Physics obtained prior to the advent of Quantum Mechanics, together with hypotheses proposed by some of the physicists whose ideas contributed to Hypersphere World-Universe Cosmology (WUC) from the seventeenth through the twentieth centuries. These results and ideas are then unified into a single coherent framework within the developed WUC.
Category: Relativity and Cosmology
[1570] ai.viXra.org:2606.0027 [pdf] submitted on 2026-06-10 20:42:04
Authors: Dainis Zeps
Comments: 19 Pages. (Note by ai.viXra.org Admin: This submisison may not fall within the scope of ai.viXra.org and is sucject to removal)
The emergence of large language models has revealed a broader problem that extends far beyond artificial intelligence itself: contemporary political discourse increasingly lacks stable conceptual foundations. Public debates often evolve into endless cycles of reinterpretation, rhetorical adjustment, and ideological reformulation, producing large volumes of commentary while generating little cumulative understanding. The same tendency can be observed in AI-generated political reasoning, where internally consistent narratives may drift away from observable reality.This paper proposes an alternative methodology based on the systematic use of prompts as explicit working assumptions. Rather than beginning with arguments, participants begin with prompts that function as provisional axioms. The objective is not to win a debate but to construct increasingly coherent prompt structures capable of organizing observation, interpretation, and judgment. New prompts emerge from previous ones, forming a dynamic framework for collective reasoning.As a test case, the paper examines the problem of contemporary Russia and the future of the Russian imperial system. Beginning from the prompt that the federalization and demilitarization of Russia should become a recognized objective of Western policy, the discussion develops a sequence of related prompts concerning imperial structures, social organization, human agency, fear, coercion, and the relationship between state preservation and human well-being. Particular attention is given to the possibility that the principal victims of imperial systems may be the populations living within them, and that conventional geopolitical discourse often obscures this perspective.The paper does not seek to provide definitive political conclusions. Instead, it explores whether prompt-based discourse can serve as a more productive and reality-oriented alternative to conventional political argumentation. The Russian question is therefore treated not only as a geopolitical problem but also as an experimental domain for investigating new forms of structured collective reasoning in the age of artificial intelligence.
Category: Social Science
[1569] ai.viXra.org:2606.0026 [pdf] submitted on 2026-06-10 20:39:26
Authors: Ian Litchfield
Comments: 5 Pages. (Note by ai.viXra.org Admin: This submission may not be written in a scholarly manner as required - Please conform and cite and list scientific references)
The foundational crisis of modern physics stems from the treatment of space-time as a smooth mathematical continuum. By replacing this abstraction with a granular, emergent quantum lattice, we can eliminate the mathematical infinities of General Relativity (GR) and reconcile it with Quantum Mechanics (QM). This framework proposes that space-time possesses a physical structure with variable coupling efficiency regulated by density, providing a single, unified mechanism for several of the greatest mysteries in astrophysics
Category: Relativity and Cosmology
[1568] ai.viXra.org:2606.0025 [pdf] submitted on 2026-06-10 20:36:58
Authors: Russell S. Clark II, Brian L. Swift
Comments: 84 Pages. This paper is intended to describe a research program and causal topology framework toward an improved formulation of the cosmological constant problem.
This integrated draft is a research-program white paper that harmonizes three strands of the Causal Topology Vacuum Model (CTVM): the broad v7 dark-sector program, the shorter v8 corrective scaffold, and the Volovik/statistical-sector revision. The central claim is no longer that CTVM has been derived as a theorem of algebraic quantum field theory (AQFT). The corrected claim is more precise: CTVM is a layered, testable framework in which regulated vacuum correlations are separated into operational response sectors, encoded by response-weighted representable matroids, and conditionally related to gravitational sourcing through a separate semiclassical or holographic dictionary. Version 15.5 retains the referee-facing viability improvements and critical-path improvements: a tighter dependency schema, a modular-compatibility status note, a compact SK-versus-CPTP worked example, an explicit matroid falsifier, clearer Volovik analogy boundaries, and more visible falsifier/non-claim summaries. First, the transport—teleportation diagnostic is rewritten as operational prose rather than as a numbered pseudo-equation, while preserving the distinction between path-dependent geometric response and resource-mediated algebraic relabeling. Second, the near-degenerate horizon-edge assumption is strengthened into a spectral-shell hypothesis with an explicit expansion parameter for the approximation γ+ ≃ γ−. These are deliberately clarifying revisions; they sharpen presentation, operational falsifiability, and horizon-edge kinetics without adding new load-bearing claims. Version 15.5 further tightens the architectural-tradeoff statement and quarantines the conditional residual-sector construction: a thresholded binary reduction of the residual response block, a matroid-to-CSS code ansatz, a quantified addressability/leakage trade-off, a small three-detector CSS illustration, and an analytic longitudinal-mode asymptotic in Appendix H.12. These additions are framed as construction targets and calculable hypotheses, not as completed proofs of residual gravitational inertness. Version 15.5 also retains a modular-equivalence consistency check motivated by the companion Entropic Inertia analysis: if inertia is a Rindler modular work response, then any sector excluded from gravitational sourcing must also be absent from the inertial modular-work functional, or else the Einstein equivalence principle would be violated. This is stated as a conditional sector-matching principle, not as a proof of the equivalence principle.
Category: Relativity and Cosmology
[1567] ai.viXra.org:2606.0024 [pdf] submitted on 2026-06-09 20:41:07
Authors: John Smith
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please use real author name; please cite and list scientific references)
Within the contemporary intersection of the sociology of knowledge and higher education psychology, the friction between academic agents and rigid macro-structures (e.g., peer-review frameworks, repository compliance audits, institutional tenure-track metrics) has grown increasingly severe. Traditional literature regarding "Academic Burnout" or "Institutional Stress" routinely relies on linear, binary reductionism. It simplifies scholars into passive, stress-enduring economic units, thereby completely overlooking the unique, hyper-rationalized cognitive architecture inherent to intellectual cohorts.This study asserts a distinct alternative: Scholars, as professional investigators and deconstructors of systemic rules, exhibit a hyper-intellectualized mode of psychological defense when confronting the structural backlash and frustrations imposed by social or institutional boundaries.To map this recursive mirror phenomenon, this paper introduces concepts from Information Theory and Cybernetics to construct a "Five-Fold Sovereign Matrix," strictly bounded by the mathematical equilibrium of the Fibonacci sequence (Fu2085=5). This model demonstrates that when an individual mind encounters systemic blockades, the neural architecture spontaneously collapses and converges into one of five baseline defense archetypes to preserve internal thermodynamic equilibrium (homeostasis) against physical reality. By shifting the perspective from clinical pathology to functional systemic states, this framework provides a powerful, de-stigmatized path toward safeguarding cognitive sovereignty for frustrated intellectuals.
Category: Social Science
[1566] ai.viXra.org:2606.0023 [pdf] submitted on 2026-06-09 20:23:35
Authors: Sudipto Chandra
Comments: 7 Pages. Creative Commons Attribution-NonCommercial 4.0 International
Between 2022 and 2026, commodity bot mitigation shifted from binary, single-signal blocklisting toward composite trust scoring: a request is admitted only if it satisfies a conjunction of independently evaluated detection layers. Cloudflare, which fronts a large share of all sites that deploy bot-mitigation tooling, exemplifies this architecture with a stack we decompose into fifteen layers grouped into five domains — network and transport, client environment, behavioral, interactive challenge, and programmable-cryptographic controls. This paper offers a defender-oriented taxonomy of that stack. For each layer we characterize the signal it reads, the structural reason it is or is not evadable, and the residual hardness that remains after best-effort evasion. Our central observation is that evadability is not uniform: layers that read artifacts a client emits (TLS handshakes, HTTP/2 frame ordering, header order) are structurally weak because the artifact can be reproduced exactly, whereas layers that read properties a client must continuously possess (genuine per-zone behavioral history, a privately held cryptographic credential) resist forgery by construction. We argue that the long-run defensive trajectory follows from this asymmetry, and that newer mechanisms such as cryptographic agent attestation are a different kind of control altogether: forgery-resistant by construction. Their present weakness is not cryptographic but a matter of deployment, since current configurations fail open when no signature is presented.
Category: Artificial Intelligence
[1565] ai.viXra.org:2606.0022 [pdf] submitted on 2026-06-08 01:19:11
Authors: Mohammed Belabbaci
Comments: 5 Pages.
The IEEE 754 floating-point standard, foundational to modern computing since 1985, treats division by zero as an undefined operation, returning error states or special infinity values. This convention, while practically expedient, creates mathematical discontinuities and computational barriers across multiple domains. We propose IEEE DZ20i, a continuous extension of IEEE 754 based on the axiom a/0 = a, which maintains computational continuity through zero-valued divisors.This paper presents the mathematical foundation of the DZ20 axiom, demonstrates its consistency within a Meta-Framework for Adapted Mathematics (MCMA), specifies the IEEE DZ20i standard including symmetric human-AI co-validation mechanisms, and explores applications across algorithmic computing, energy systems, hardware design, robotics, and space exploration.Implementation results show that IEEE DZ20i eliminates a broad class of runtime exceptions while preserving backward compatibility with IEEE 754 operations outside the zero-divisordomain.
Category: Mathematical Physics
[1564] ai.viXra.org:2606.0021 [pdf] submitted on 2026-06-07 19:03:00
Authors: E. P. J. de Haas
Comments: 29 Pages. https://doi.org/10.5281/zenodo.20583983
Starting from the minimal complex matrix algebra M2(C), this paper shows that two biquaternion products suffice to derive the complete conservation structure of a relativistic perfect fluid and its dilatation current, without postulating a Lagrangian and without invoking Noether's theorem as an external tool.The product M = R^T G, formed from the spacetime position four-vector R and the energy-momentum four-vector G, decomposes automatically into the action density, angular momentum density, and moment-of-energy density as algebraically forced channel outputs. The closure condition dM = 0 packages all three conservation laws into a single Maurer-Cartan flatness condition on a Lie-algebra-valued current in the adjoint representation of the Lorentz group, a structure that follows from the asymmetric transformation law of the biquaternion transpose and requires no additional input.The perfect-fluid reduction projects M onto the adjoint orbit of the fluid velocity, yielding the relativistic Lagrangian fluid equations in comoving coordinates whose gamma-scaling encodes the dilatation structure of the flow. A companion product J_D = R(U^T G) constructs the dilatation current explicitly: under the perfect-fluid constraint it reduces to J_D = eR, a pure Lorentz four-vector whose conservation is the relativistic virial theorem and whose sole surviving constraint in the thin-disk limit is the Euler homogeneity relation div(r) + 1 = 0 — the differential signature of a renormalisation-group fixed point, derived here without assuming scale invariance.The construction demonstrates that the Lagrangian, the Euler-Lagrange equations, and the Noether currents are outputs of the algebraic structure of M2(C) rather than its foundation, and identifies the biquaternion transposed product as the minimal algebraic operation from which the standard framework's results follow as necessary consequences.
Category: Relativity and Cosmology
[1563] ai.viXra.org:2606.0020 [pdf] submitted on 2026-06-08 01:15:33
Authors: Steven Elliott
Comments: 10 Pages.
The measured vacuum energy density entering cosmology is a classical macroscopic quantity. In standard quantum theory, the emergence of classicality from quantum superposition is explained through decoherence: a subsystem loses accessible phase coherence through entanglement with environmental degrees of freedom. This paper applies that same logic to the vacuum itself. An arbitrary finite spherical region of vacuum is treated as an interior quantum subsystem, while its boundary and exterior vacuum degrees of freedom form its environment. Under a holographic assumption, the boundary carries an area-scaling information capacity and functions as the interface through which interior field configurations are encoded relative to the exterior. Tracing over the boundary-exterior environment yields a reduced density matrix for the interior whose off-diagonal components are suppressed by environmental overlap factors. In a Gaussian influence-functional model, the decoherence exponent is controlled by a boundary noise kernel and scales schematically with the number of boundary information cells, Γij ∝ A/ℓP2, for distinguishable interior configurations. Thus a finite vacuum region cannot be treated as a pristine, perfectly coherent, isolated quantum register. The global vacuum may remain pure, but every finite restriction of it is generically mixed and dynamically decohered by the rest of the vacuum. This vacuum self-decoherence does not by itself calculate the observed cosmological constant. It instead establishes that a finite vacuum region is never operationally described by an unlimited pristine coherent state. This provides a possible physical mechanism underlying the coarse-graining that renormalization implements algebraically.
Category: Quantum Physics
[1562] ai.viXra.org:2606.0019 [pdf] submitted on 2026-06-08 19:19:38
Authors: Hacı Soğukpınar
Comments: 26 Pages. (Note by ai.viXra.org Admin: Further repetition may not be accepted)
The origin of mass remains one of the central questions in modern particle physics. Within the Standard Model, particle masses arise through spontaneous electroweak symmetry breaking and Yukawa interactions with the Higgs field. While the discovery of the Higgs boson provided strong experimental support for this framework, the Standard Model does not explain the numerical values of fermion masses, the origin of Yukawa couplings, or the observed mass hierarchy spanning several orders of magnitude. Unified Fractal Quantum Field Theory (UFQFT) proposes an alternative interpretation in which mass emerges from localized resonance energy generated by coupled energy (Φ) and charge (Ψ) fields embedded within a critical fractal spacetime characterized by an effective dimension near D ≈ 2.7. In this work, we perform a systematic comparison between the Higgs mechanism and resonance-based mass generation. The analysis examines the origins of gauge-boson masses, fermion masses, and nucleon mass within both frameworks. Particular attention is given to the role of Yukawa couplings, resonance stability, fractal confinement, and energy localization. We show that while the Standard Model successfully parameterizes observed particle masses through Higgs interactions, UFQFT provides a geometric interpretation in which mass emerges from resonance organization rather than from independent coupling constants. The conceptual foundations, mathematical structures, predictive capacities, and experimental implications of both approaches are compared. The study establishes a framework for evaluating whether resonance geometry can reproduce known mass phenomena while providing new insights into the hierarchy problem, flavor structure, and the physical origin of mass. This comparison constitutes an important component of the broader UFQFT Standard Model Validation Program and contributes to the ongoing search for a deeper understanding of matter and mass generation.
Category: High Energy Particle Physics
[1561] ai.viXra.org:2606.0018 [pdf] submitted on 2026-06-07 17:14:13
Authors: Nigel B. Cook
Comments: 10 Pages. (Note by ai.viXra.org Admin: An abstract labeled as such is required in the article; please cite and list scientific references)
There are three roads to the same mechanism for quantum gravity given in 2011 vixra paper 1111.0111. This paper extracts them from that paper and compares them. Illustrations are appended. Paper was checked using Microsoft Copilot AI system for mathematical accuracy.
Category: Quantum Gravity and String Theory
[1560] ai.viXra.org:2606.0017 [pdf] submitted on 2026-06-07 17:08:30
Authors: Xiangqian Zhang，Mingming Zhao，Linchao Ge
Comments: 5 Pages.
This paper systematically analyzes the geometric origins of errors within Topological ResidualTheory (TRT). Taking the Fibonacci number Fu2081u2089 = 4181 as the critical node, we demonstrate thatthe fine-structure constant α is precisely the radian-measure expression of the angle 0.4181°. Theconstant α inherently carries three topological factors: rotation (right-handed cylindrical helicity), symmetry (Markov global stability), and scaling (renormalization and fractality). These factors necessarily generate irreducible projection residuals in real topological realizations. By quantifying the discrepancies between TRT predictions and both 1/137 and experimental values for α, G = μu2080 α², and the Planck constant, we show that all observed errors originate from the intrinsic rotation and topology of α itself. Special emphasis is placed on the multiple algebraic decompositions of 4181 and on relating error magnitudes to the renormalization factor (1/2)α² × 10u207f or α² × 10u207f. Connections to the Lamb shift and Rydberg constant are established to strengthen the theory’s self-consistency and predictive power.
Category: Mathematical Physics
[1559] ai.viXra.org:2606.0016 [pdf] submitted on 2026-06-06 13:24:06
Authors: Ginanjar Utama
Comments: 8 Pages.
This paper proves, by explicit Clifford-algebra computation, that the γ0-diagonal complete orthogonal primitive decomposition of real Cl(1,3) has two sectors, while the extension to Cl(1,4) supplies a second independent commuting basis-blade involution, γ1234. Because I5 = γ0γ1234, the generated involution group is Z2 × Z2, not (Z2)3. The resulting decomposition contains four primitive idempotents, each generating a real 8-dimensional minimal left ideal. The count four is itself fixed by Wedderburn theory, since each simple summand has rank two; the explicit content of the result is the basis-blade realization of the family and the demonstration of why a naive three-involution count would predict eight. The central idempotents (1 ± I5)/2 realize the real semisimple splitting Cl(1,4) ≅ M2(H) ⊕ M2(H), where H denotes the quaternions. They do not, by themselves, supply a complex imaginary unit; a complex spinor interpretation still requires choosing an internal quaternionic complex structure within each ideal. Physical identifications with chirality, charge, helicity, or U(1) phase are therefore treated as conjectural.Supporting results include: (i) a Pancharatnam-phase computation from projector triple products in Cl(3,0), confirming the half-solid-angle rule 2|φ| = Ω for geodesic spherical triangles; (ii) a bivector-square classification of geometric-i candidates, with the observation that the chiral split in real Cl(1,3) is a complex-structure operation, not a real idempotent split; and (iii) a short positioning of the result relative to real Cl(0,6) and complex Clu2086 Standard Model programs. The paper is intended as a lower-dimensional real-idempotent audit, not as a derivation of a Standard Model generation.
Category: Mathematical Physics
[1558] ai.viXra.org:2606.0015 [pdf] submitted on 2026-06-07 00:27:21
Authors: Rüdiger Giesel
Comments: 21 Pages.
Weformulate a particle-physics sector in an octonionic projection framework in which the Standard Model is interpreted as the low-energy associative projection of a deeper non-associative field dynamics. The fundamental objects arethree octonion-valued fields ΨI ∈ O, I = 1,2,3, whose non-associative content is measured by the octonionic associator [Ψ1,Ψ2,Ψ3] = (Ψ1Ψ2)Ψ3− Ψ1(Ψ2Ψ3). A positive semidefinite associator potential dynamically suppresses nonassociative excitations at low energies and selects local associative subalgebras. We show how the chain O → Hphys → C motivates the emergence of complex quantum fields and Standard-Model-like residual gauge sectors related to SU(3)c, SU(2)L, and U(1)Y. We emphasize that the exact chiral hypercharge spectrum is not derived here; it requires an explicit projector representation.In this construction the associator is not merely an algebraic obstruction, but a dynamical source for projection, symmetry breaking, generation structure, mass hierarchy corrections, neutrino mixing corrections, Higgs-sector deformations, and possible fifth-force phenomenology. We briefly distinguish this proposal from division-algebraic Standard-Model reconstructions, where octonions primarily encode particle representations and charge assignments; here the new ingredient is the promotion of the associator to a field-theoreticquantity. The framework provides a constrained octonionic projection mechanism leading to Standard-Model-like particle sectors, while the complete derivation of the observed chiral charge spectrum remains an open task.
Category: Relativity and Cosmology
[1557] ai.viXra.org:2606.0014 [pdf] submitted on 2026-06-06 03:46:27
Authors: Xiangqian Zhang, Mingming Zhao, Linchao Ge
Comments: 13 Pages.
Within the framework of Topological Residual Theory (TRT), this study explores the unification ofgravitational and electromagnetic interactions at the level of spacetime geometry. Utilizing the cylindrical helical motion of spatial points (geometrization of Zitterbewegung) as the dynamical foundation, we derive the wave equationvia the variational principle of the displacement field . Using the geometric structure of thelocal cylindrical orthonormal frame induced by local helical symmetry, the electric, magnetic, and gravitational fields are defined as projections of the time derivatives of onto this orthonormal frame. Consequently, the mutual orthogonality of the three fields emerges as a geometric necessity of the frame decomposition rather than an independent postulate. The gravitational field is derived via two independent pathways: (i) the framekinematics and time evolution pathway ( ), and (ii) the second-order derivative pathway of the wave equation ( ). The mathematical consistency betweenthese two pathways indicates that gravity can be interpreted as a second-order residual effectof electromagnetic oscillations propagating at the speed of light. Furthermore, charge is defined as the topological charge (winding number / Hopf invariant) of the helical displacement field on a closed sphere (Euler characteristic ), which manifests as the effective rate of mass change only during the transient state of topological structure formation. Under the compatibility condition of theflux change rate (local topological flux continuity), we naturally derive the vacuum relations and . Based on this unified topological mechanism, the model provides a self-consistent geometric explanation for both charge quantization and particle spin.
Category: Mathematical Physics
[1556] ai.viXra.org:2606.0013 [pdf] submitted on 2026-06-04 20:16:22
Authors: Richard Andrew Holland
Comments: 30 Pages.
We present an efficient and consistent method for discerning preferable and generating functions of data using filtered spectral fingerprints. Spectral analysis of functions and data is hardly new. For example, with Fourier Transforms one can classify and identify functions using coefficients. The problem is that statistical, domain and systematic error noise is baked into the spectrum of coefficients. For over two centuries Legendre polynomials have been used for spectra, however, we are unaware of prior use of this approach. We create a hash library of function spectra to quickly find preferable and/or generating functions. Software tools (Patents Pending) have been developed utilizing this methodology, including one for finding AI/ML Neuron Activation functions. Even for noisy and instrument biased data, researchers and machine optimizers can better discern preferential and underlying functions that generate noisy data. Preliminary AI/ML results are also presented.
Category: Functions and Analysis
[1555] ai.viXra.org:2606.0012 [pdf] submitted on 2026-06-04 21:50:22
Authors: Brent Hartshorn
Comments: 22 Pages.
This paper introduces a phased, trans-boundary framework for arresting the public-health dust hazard of the desiccating Salton Sea while recovering critical minerals from imported marine water. Decades of "Sea-to-Sea" proposals to import water from the Gulf of California have foundered on three obstacles repeatedly identified by independent state review: tens of billions of dollars in cost, multi-decade timelines, and the ecological damage of discharging concentrated brine back into the Gulf. We propose the "Biotic—Thermal Vapor Pump" (BTVP), sited in the below-sea-level Laguna Salada basin of Baja California, Mexico, whose central innovation directly removes the brine-discharge obstacle. Phase I couples a scale-asymmetric halophytic canopy (Avicennia germinans and Rhizophora mangle) to a recently demonstrated additive-free, brine-discharge-free solar-thermal evaporator (laser-textured superwicking black metal) that recovers nearly all dissolved salts—and, via embedded hydrogen-titanate nanoparticles, lithium—as solid product rather than as toxic concentrate, converting the terminal-basin salt-disposal liability into a managed resource stream. Phase II incorporates deep, closed-loop downhole heat exchangers to safely tap the underlying 187◦ C geothermal reservoir without phreatomagmatic or halite-hydrolysis hazard, and to access the lithium-rich (∼100—300 mg/L) native geothermal brine of the "Lithium Valley" resource. Phase III integrates a DNA-inspired pyrimidone Molecular Solar Thermal (MOST) matrix asa timing actuator for on-demand vapor pulses. We present coupled mass, salinity, thermodynamic, andatmospheric models, and—critically—bound each subsystem against the relevant physics. The dominant, defensible benefits are dust suppression, brine-free salinity management, and critical-mineral recovery; we show by moisture-budget and recycling-ratio analysis that the local atmospheric contribution to down-wind precipitation is a small, bounded effect rather than a primary water-supply mechanism, and we present it as such. Finally, we frame the design as Stage 1 of a two-stage program: an independently beneficial Mexican-basin installation that proves the brine-free zero-liquid-discharge desalination chain and thereby makes credible a Stage 2 in which the same technology—answering the decisive brine-discharge objection that ended prior state review of Gulf importation—enables direct stabilization of the Salton Sea itself.
Category: Climate Research
[1554] ai.viXra.org:2606.0011 [pdf] submitted on 2026-06-04 04:48:52
Authors: Stephen P. Smith
Comments: 11 Pages.
The search for a unified ontology has long been divided between mathematical descriptions of external structure and phenomenological accounts of lived experience. This paper argues that an unexpected bridge between these domains may already exist within the elementary axioms of Lie algebra. The antisymmetry of the Lie bracket expresses a fundamental principle of two-sidedness, while the Jacobi identity introduces an irreducible triadic relation that stabilizes this polarity through algebraic closure. Together these axioms suggest a primitive logic of reciprocity and homeostasis that precedes geometric realization and therefore exists conceptually prior to spacetime structure. Building upon this observation, the paper explores structural correspondences between Lie algebra, Peircean semiotics, Friston's free energy principle, Hegelian dialectics, and CPT-symmetric cosmological models. In each case, a common pattern emerges: an initial unity gives rise to a dyadic tension whose persistence requires mediation by a third term capable of restoring coherence without eliminating difference. The resulting triadic structure functions as a homeostat, regulating relations across scales while preserving the integrity of the participating elements. The paper proposes that this recurring pattern may represent a scale-invariant principle of organization. While not offered as a physical theory, the framework provides a conceptual ontology in which meaning, symmetry, homeostasis, and semiosis emerge from a common relational architecture. The central thesis is that two-sidedness and triadic homeostasis are not late products of biological or cognitive evolution but may instead constitute primordial conditions for the existence of stable relational order.
Category: General Science and Philosophy
[1553] ai.viXra.org:2606.0010 [pdf] submitted on 2026-06-04 19:54:57
Authors: Nico Kleff
Comments: 8 Pages. (Note by ai.viXra.org Admin: Some texts in Table 1 are cutoff!)
The Alcubierre warp metric requires negative energy density distributed around a spacecraft hull. We propose a conceptual architecture in which a spacecraft hull consists of a large-area array of nano-fabricated Casimir cavities, each within Ford-Roman quantum-inequality bounds, collectively producing an integrated negative energy density profile approximating the spatial boundary conditions of the Alcubierre metric. Segmented, addressable piezoelectric control of hull panels is proposed as a mechanism for dynamic shaping of the metric distortion, addressing the internal-controllability problem of the original warp-bubble scheme. We outline a six-layer nanofabrication stack (SiC substrate, TiN adhesion layer, Au conductor, Au-lined trench array, graphene monolayer, Al2O3 encapsulation), a scaling hypothesis linking per-tile Casimir output to hull-integrated negative energy density, and a four-phase experimental roadmap. No claim is made that the scheme will succeed; the contribution is a concrete, testable structural hypothesis connecting established Casimir physics to the open engineering problem of warp-metric generation.
Category: Relativity and Cosmology
[1552] ai.viXra.org:2606.0009 [pdf] submitted on 2026-06-03 20:02:38
Authors: Haoxiang Yu
Comments: 11 Pages. See https://github.com/yhx-12243/Sidon3 for formalization
We determine the exact value of the Sidon constant of the four-element set {0,1,2,3} to be 5/3. The lower bound was established by Neuwirth via an explicit family of trigonometric polynomials; we prove the matching upper bound. Our proof introduces a new method: given a point on the unit circle we construct a cubic self-inversive polynomial whose three roots lie on the unit circle, extract positive real weights from these roots, and use a weighted square-sum identity to obtain the sharp estimate. The entire proof is formalized in Lean 4 using mathlib.
Category: Functions and Analysis
[1551] ai.viXra.org:2606.0008 [pdf] submitted on 2026-06-03 19:50:46
Authors: James Francis Godwin
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
This paper proposes a cosmological framework in which the universe as we know it — one in which time exists and flows — is paired with a companion universe in which time does not exist. Analogous to the quantum mechanical creation and annihilation of particle/antiparticle pairs, these two universes came into existence together at the Big Bang from nothing, and will eventually annihilate each other, returning to nothing. The expansion of the temporal universe continuously stretches the timeless companion, which resists this stretching and exerts a restoring force. This paper proposes that this restoring force is the origin of gravity, and that the gravitational constant G is not truly constant but increases over time as expansion proceeds. This single underlying principle is shown to offer natural explanations for gravity, dark matter, quantum entanglement, wave-particle duality, the nature of light, the origin of supermassive black holes, the anomalous brightness of early galaxies observed by JWST, and an alternative interpretation of cosmological redshift that removes the need for dark energy. The framework prioritises simplicity and testability, and makes specific predictions that differ from the standard cosmological model (ΛCDM).
Category: Relativity and Cosmology
[1550] ai.viXra.org:2606.0007 [pdf] submitted on 2026-06-02 21:04:11
Authors: Fusao Ishii
Comments: 26 Pages.
This paper derives two landmark predictions of quantum electrodynamics—the anomalous magnetic moment of the electron (g−2) and the Lamb shift of hydrogen—from the stochastic Coulomb field framework established in Papers 1—4 [1—4]. Both effects have the same physical origin: the zero-point radiation field (ZPF), derived in Paper 1 from the Coulomb virtual photon cloud via the Boltzmann ergodic theorem (proved in Paper 3 [3]), modifies the electron trajectory in two distinct physical situations. For the anomalous magnetic moment: the ZPF modifies the radius of the Zitterbewegung helix established in Paper 4, producing a correction to the bare g = 2 result. Integrating the ZPF spectral density SE(ω) = ℏω^3/6π^2ϵ0c^3 weighted by the time-ordering factor of the emission-reabsorption process gives the Schwinger term: ae ≡ (g − 2)/2 = α/2π ≈ 0.001 161, in agreement with the leading QED prediction and experiment. For the Lamb shift: the ZPF drives fluctuations in the electron’s position within the hydrogen atom. These fluctuations smear the electron over the Coulomb potential of the nucleus, producing an effective shift in the potential energy. Because the Laplacian of the Coulomb potential is proportional to a delta function at the origin, only s-states (l = 0) are shifted. Using the Compton cutoff ωc = mc^2/ℏ from Paper 1 and the orbital frequency as the lower cutoff, the energy shift of the 2S1/2 level is: ΔνLamb ≈ 1 040 MHz, compared with the experimental value of 1057.845 MHz—agreement to within 2% at first order. Together these results confirm that the stochastic Coulomb field framework reproduces the two most celebrated predictions of QED from purely classical foundations.
Category: Quantum Physics
[1549] ai.viXra.org:2606.0006 [pdf] submitted on 2026-06-02 20:55:35
Authors: Hacı Soğukpınar
Comments: 45 Pages.
The Unified Fractal Quantum Field Theory (UFQFT) proposes a resonance-geometric framework in which matter, interactions, spacetime, and cosmology emerge from the dynamics of two fundamental fields: the energy field (Φ) and the charge field (Ψ), embedded within a fractal spacetime characterized by a critical effective Hausdorff dimension of D ≈ 2.7. In this paradigm, elementary particles are not fundamental point-like entities but stable resonance configurations of coupled Φ—Ψ fields, while mass, charge, spin, and particle stability arise from fractal resonance structure and dimensional localization. The theory identifies D ≈ 2.7 as a critical threshold at which confinement, long-range interactions, temporal evolution, and stable matter coexist, providing a unified geometric explanation for the emergence of ordinary matter, dark matter, dark energy, and the arrow of time. Gravity is reinterpreted as an emergent symmetry-restoring response of the fractal field, whereas electromagnetic, weak, and strong interactions arise from distinct resonance modes and topological transitions of the same underlying field system. UFQFT further extends naturally to nuclear structure, halo nuclei, neutrino oscillations, CP violation, baryogenesis, black-hole interiors, neutron stars, and bubble cosmology, offering a common geometric origin for phenomena traditionally described by separate theoretical frameworks. A scale-dependent dimensional flow from microscopic fractal regimes to macroscopic classical geometry establishes a UV—IR bridge linking particle physics with cosmological structure formation and large-scale dynamics. The framework yields a broad range of experimentally testable predictions, including fractal corrections to particle lifetimes and scattering processes, modifications to neutrino oscillation patterns, sub-millimeter deviations from Newtonian gravity, distinctive signatures in halo nuclei, scale-dependent suppression of the cosmological matter power spectrum, non-standard gravitational-wave propagation, and observable imprints in future cosmological surveys and precision laboratory experiments. Collectively, UFQFT suggests that the Universe is fundamentally a hierarchy of resonant geometric structures rather than a collection of elementary particles and forces, providing a unified and falsifiable pathway toward the geometric unification of quantum physics, gravitation, and cosmology.
Category: Astrophysics
[1548] ai.viXra.org:2606.0005 [pdf] submitted on 2026-06-02 20:49:59
Authors: Filippo Leone
Comments: 14 Pages. (Note by viXra Admin: An abstract in the article labeled as such is required; please cite and list scientific references)
The present work proposes a phenomenological framework describing dynamical processes potentially leading to the formation of localized, self-sustaining, metastable energy configurations depending on the vacuum recombination processes, hereafter referred to as Localized Energy Configurations (hereafter referred to as LEC for brevity). Depending on the surrounding dynamical conditions, such configurations may exhibit either expansive or mass-like behavior.This work does not intend to present a complete physical theory nor a rigorous mathematical treatment. Its purpose is to introduce a coherent conceptual framework that may constitute a possible starting point for subsequent theoretical developments.The mathematical formulations presented herein are exclusively phenomenological and descriptive in nature. Any advanced formalization within the framework of Quantum Field Theory or General Relativity lies beyond the scope of the present work.The concepts and the general structure of the model may be freely used as a basis for possible future theoretical investigations.The present work is ideally positioned as a dialogue between intuition and formalism, closer to an exploratory reflection than to a traditional academic treatment.
Category: Relativity and Cosmology
[1547] ai.viXra.org:2606.0004 [pdf] submitted on 2026-06-02 00:36:21
Authors: Carlos Mauricio Santacruz Elizondo
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The Theory of the Empty Universe (TEU) proposes that gravity emerges from a differential deformation of space-time. In this framework, particles preserve an internal deformation state associated with their formation epoch, while the external vacuum continues to deform as the universe expands. This article develops a preliminary phenomenological model connecting ancient-photon solar-deflection residualswith an effective photon gravitational susceptibility and a time-dependent gravitational coupling. Motivated by the high-redshift quasar 0229+131 and the comparisonsource 0235+164, the observed residual is represented by a dimensionless parametes.
Category: Relativity and Cosmology
[1546] ai.viXra.org:2606.0003 [pdf] submitted on 2026-06-01 20:12:31
Authors: Moninder Singh Modgil, Dnyandeo Dattatray Patil
Comments: 10 Pages.
We construct a unified mechanism in which Electrical Energy Extraction by Rotation of Earth via Torsion (EEERET) acts as the control parameter of a phase-transition-like dynamical system whose order parameter is the sign of large-scale rotation. The construction proceeds in five steps. First, in a rotating background of GRBMORS type (G¨odel—Rindler—Brahe—Maxwell—Obukhov—Randall—Sundrum), the relative daily angular velocity between the Earth and the cosmological frame sources a torsion-induced four-current JμI . Second, this currentfeeds the covariant Maxwell equations and drives an instability whose pseudoscalar invariant I2 = Fμν e Fμν grows secularly. Third, the pseudoscalar invariant defines an effective electromagnetic chemical potential μEM that tilts the symmetric Mexican-Hat potential governing the rotational order parameter R and renders rotation reversal directed rather than symmetric. Fourth, when μEM crosses the cusp-catastrophe threshold |μc| = (8/3 √3)λR30 thebarrier collapses, producing the rapid rotation-reversal (RRR) regime, distinct from the gradual rotation-reversal (RR) regime in which a finite barrier survives. Fifth, the construction is shown to be frame-equivalent: the sameobservable consequences obtain whether one treats the Earth as rotating in a non-rotating cosmos, or treats the universe as rotating around a non-rotating Earth, because only the relative angular velocity Ωrel = ΩE − ΩUenters the source term. We give explicit RR and RRR onset times, indicate the role of a superconducting loop as a coherent realization of the mechanism, and list observational and laboratory signatures. The framework relies on, and complements, the chiral wave-function and conformally compactified Romano—Goebel construction developed in a companion preprint.
Category: Relativity and Cosmology
[329] ai.viXra.org:2607.0057 [pdf] replaced on 2026-07-27 07:37:08
Authors: Tomasz Kobierzycki
Comments: 41 Pages.
This paper proposes an extension of Lorentz spacetime symmetry from the usualconnected domain of an ordinary observer to four orientation sectors defined by one andthe same invariant null boundary. The motivation is that the standard Lorentz groupdescribes all finite boosts available inside a chosen causal sector, but it does not by itselfsupply a real clock—ruler description of the neighbouring non-null domains separated fromthat sector by lightlike directions. The proposed extension completes this local orientationstructure without accelerating ordinary matter through the speed of light and withoutintroducing additional spacetimes. Every observer still has one real time axis and threereal spatial axes. The distinction between sectors is which non-null direction supplies theobserver’s clock and which three directions form its rest space.The local speed of light remains exactly equal to c in every sector. This is not imposedby assigning a different limiting velocity to each description; it follows because all sectorframes share the same null set and their admissible transformations preserve that set.Ordinary Lorentz boosts then describe motion inside any fixed sector, while the sectorextension describes the four possible causal orientations of the complete local frame. Aside sector is therefore not a superluminal state of ordinary matter. It is a Lorentzianframe in which one direction regarded as spatial by an ordinary observer supplies the singlelocal time axis, whereas the inherited ordinary time direction belongs to the side observer’sspatial rest space. Proper time remains real and future-directed, and a change of sectorchanges the clock—ruler decomposition rather than reversing or discontinuously replacingthe physical worldline.The same principle is generalised to curved spacetime by applying the sector structureto local orthonormal coframes and to the proper geometric scales on which a general-relativistic solution depends. When the scale used by one chart reaches its null boundary,the neighbouring sector evaluates the same gravitational field with the reciprocal activescale and with the corresponding sector metric. The purpose is to replace an extrapolationtoward a vanishing, singular scale by a geometrically regular continuation whose curvatureand causal distance can be tested directly. The resulting picture is one spacetime equippedwith a four-sector Lorentz atlas: local causality and the invariant light speed are preserved,while black-hole and cosmological limits can be re-examined as boundaries of sectordescriptions rather than being assumed in advance to be physical singular endpoints
Category: Relativity and Cosmology
[328] ai.viXra.org:2607.0044 [pdf] replaced on 2026-07-16 04:47:03
Authors: Lluis Eriksson
Comments: 7 pages. Machine-checked in Lean 4. Supersedes v1; proof artifact: hrpoly-cmp116-main-reduction-v0.3-2026-07-16
We give a machine-checked reduction of the finite-dimensional fluctuation integral in Balaban's CMP116 large-field analysis. Starting from the physical block constraint Q, the formal development constructs a sparse right inverse E and the constraint-elimination operator C = I - EQ. It proves QE = I, QC = 0, C² = C, the exact sparse norm ||EB|| = M^(d-1)||B||, and the volume-independent bound ||C|| ≤ 1 + M^(d-1) for d ≥ 3. An exact physical/CMP116 isometry transports C to finite Gaussian coordinates without norm loss. The same development constructs the physical localization projector P_Z0, evaluates the complex quadratic Gaussian, localizes its determinant to rank |I(Z0)|, performs the outer Gaussian integration, and absorbs both costs into an explicit exp(c|Z0|) factor.Two corrections exposed by formalization are central. First, the useful domination occurs after Gaussian integration rather than through an unavailable pointwise supremum in the fluctuation field. Second, the localized quadratic matrix is A = -alpha_5 P_Z0. In the exactly identified trivial-background sector, the terminal Lean theorem inserts the concrete C, the flat Hessian, complement localization, and covariance root directly into the printed source Gamma_k = C^T Delta_k (C P_Z0^c)(C^(k))^(1/2), returning an explicit Cauchy bound without an ambient-volume factor. CMP116, however, requires the base Hessian at a generally nontrivial small background Ubar. We do not construct D²S_Wilson(Ubar) or the random-walk estimate (2.16), and therefore do not prove the physical domination, (2.26), hraw, hRpoly, a continuum limit, or a mass gap. The contribution is an auditable reduction that closes the constraint and Gaussian layers and identifies the first genuinely missing interacting construction.
Category: Mathematical Physics
[327] ai.viXra.org:2607.0039 [pdf] replaced on 2026-08-01 15:44:49
Authors: Lluis Eriksson
Comments: 14 pages. Revised and expanded v2; Lean 4/Mathlib formalization with 177 audited declarations. Companion archive SHA-256: CF8B66910C0133804E7F0E8B0F0F5D59A43211A7F445A3E33C3E04E792BC7F7B.
We present an end-to-end Lean 4/Mathlib formalization of the exact evaluation of the two-dimensional SU(2) heat-kernel lattice model on certified finite combinatorial disk cellulations. The development starts from normalized Haar probability on the concrete matrix group SU(2). It identifies its transport to S^3 with the canonical spherical measure, proves an all-order orbital integration formula, derives translated character convolution, and passes from finite character sums to the infinite heat-kernel semigroup by dominated convergence. A genuine shared-edge integral then yields the two-face Migdal move.The geometric layer is independent of any reduction tree. A cellulation stores vertices, paired half-edges, cyclic face words, incidence, Euler characteristic, and positive face areas. Connected dual graphs admit certified elimination schedules, every valid schedule reduces to the heat kernel at total area, and all schedules give the same amplitude. For the original edge model, a rooted spanning tree produces a measurable, product-Haar-preserving gauge equivalence SU(2)^E ≃ SU(2)^(V{r}) × SU(2)^(ET). A compatible tree-cotree construction then retains the exterior holonomy rather than integrating it out. For every certified physical disk cellulation, the boundary-conditioned original-edge amplitude is exactly the SU(2) heat kernel at the total face area. Coefficient extraction gives, for every irreducible label n, the normalized exterior-boundary identity E_P[W_n(H_boundary)] = exp[-n(n+2)(sum_f t_f)/4], where H_boundary is the retained holonomy of the complete exterior boundary word. The universal record is demonstrably inhabited: a concrete three-spoke disk has (V,E,F)=(4,6,3) and derived dual graph K_3. A reproduced audit covers 177 audited declarations, explicitly including both headline theorems, and finds only propext, Classical.choice, and Quot.sound in their dependency cones. The analytic solution is classical. The contribution is a concrete kernel-checked composition from Haar measure and characters to physical edge variables, gauge fixing, tree-cotree elimination, and the exact boundary-observable endpoint.
Category: Mathematical Physics
[326] ai.viXra.org:2607.0035 [pdf] replaced on 2026-08-01 08:42:41
Authors: Lluis Eriksson
Comments: 11 pages. v2 adds a two-page supersession/scope correction, removes the stray metadata suffix Author(s), and preserves the nine-page v1. Full closure: ai.viXra:2607.0039v1.
SUPERSEDED BY AI.VIXRA:2607.0039V1 FOR THE ORIGINAL-EDGE AND TREE-COTREE CLOSURE. This replacement preserves public version 1 and corrects its publication-level scope. Version 1 establishes the compact-group analytic chain, heat-kernel reductions, schedule independence and reduced-model results, but pages 7 and 9 leave open the bridge from the post-gauge-fixed evaluator to the original-edge physical integral for arbitrary cellulations. ai.viXra:2607.0039v1 supplies the missing original-edge gauge fixing, simultaneous face-holonomy transport and compatible tree-cotree closure and is therefore the authoritative source for the full exact simple-loop area-law theorem at the stated finite two-dimensional SU(2) heat-kernel scope. Neither paper constructs four-dimensional continuum Yang-Mills theory or proves a four-dimensional mass gap. The preserved version 1 follows the two-page notice unchanged.
Category: Mathematical Physics
[325] ai.viXra.org:2607.0023 [pdf] replaced on 2026-08-01 08:44:13
Authors: Lluis Eriksson
Comments: 15 pages. v2 adds a two-page supersession/status note and preserves the 13-page v1. The successor's terminal hybrid certificate remains independently REVIEW-PENDING.
SUPERSEDED BY AI.VIXRA:2607.0089V1 FOR THE TERMINAL GLOBAL-SIGN CLAIM; INDEPENDENT REPLAY PENDING. This replacement preserves public version 1 and records the later terminal-claim paper without overstating its audit status. Version 1 proves positivity of F_B, the ratio sign for 0 < beta <= 3, exact bridge and single-Bessel reductions, certified negative results, asymptotic structure and a two-scale closure map; pages 11-13 leave the global sign as a quantified conjecture. ai.viXra:2607.0089v1 claims the global ratio-monotonicity theorem through exact identities and outward-rounded interval certificates. It supersedes this record for that terminal claim, but independent replay of every exact-to-Arb handoff and interval regime remains pending in this audit. No PASS is inferred from a printed or green transcript alone. The preserved version 1 follows the two-page notice unchanged.
Category: Mathematical Physics
[324] ai.viXra.org:2607.0021 [pdf] replaced on 2026-07-14 20:04:41
Authors: Jason Merwin
Comments: 20 Pages. A GitHub repository link is provided
We demonstrate that gravitational and quantum dynamics can be unified as emergent consequences of strictly bounded computational bandwidth within a discrete generative spacetime (the Discrete Emergent Universe). In this framework, the fundamental phenomena of physics arise from scheduler load: persistent topological defects impose chronic bandwidth demand (analogous to gravitational mass), while acute logical conflicts trigger saturation-limited resolution events (analogous to quantum state collapse). Through pre-registered experiments on a growing triangulated foam, we derive a unified two-queue ledger law---governing forced backlog and standing vacuum demand---that dictates this load response with zero fitted parameters. This single internal law accurately brackets the chronic starvation collapse threshold (a gravitational-regime constant of x50 = 1.30 and completely reproduces acute Zeno-pattern suppression in temporally structured loads. While the central claim is a model-internal unification of these two operating regimes, we provide external bridge diagnostics---including a CMB amplitude basin, preliminary GW150914 ringdown-compression signatures, and formal equivalence to standard quantum and relativistic clock laws---as falsifiable targets for physical equivalence.
Category: Quantum Gravity and String Theory
[323] ai.viXra.org:2606.0072 [pdf] replaced on 2026-06-27 22:32:05
Authors: Xiangqian Zhang，Mingming Zhao，Linchao Ge
Comments: 17 Pages.
AbstractWithin the framework of Topological Residual Theory (TRT), this paper rigorously establishes thefirst-principles physical picture that "space itself flows at the speed of light along curves in a righthanded cylindrical helical form." In this picture, length and time originate from different aspects ofthe same spacetime flow motion, thereby providing a geometric explanation for the origin of theconstancy of the speed of light.To fundamentally resolve the dimensional mismatch among different physical fields that arises inclassical field theory from differing measurement protocols, we propose a Velocity-FieldRepresentation scheme: the electric, gravitational, and magnetic fields are directly defined as thethree local velocity components of the light-speed spacetime flow along the orthogonal basis of theFrenet-Serret (FS) frame [1]:This achieves a complete unification of all underlying field dimensions to velocity at the kinematiclevel. Since the flow speed of spacetime is fixed at the speed of light , different physicalinteractions essentially correspond to the allocation of this motion budget among the threeorthogonal directions: tangential propagation, normal centripetal constraint, and binormal torsion.The allocation mechanism is precisely controlled by the helical pitch angle .By introducing the time definition , we derive the first-order time-evolution equations ofthe three fields under the characteristic rotation frequencies of the FS frame (bending frequency , twisting frequency ). Under the rigid rotation of the frame, the total kineticenergy density remains strictly constant. Utilizing the rigidrotational dynamics of the frame and the vector and scalar triple-product identities, we elucidate thephysical nature by which the "self-work" terms of the rigid triad automatically vanish during rotation,thereby revealing the deep geometric mechanism of dissipation-free energy flow.The macroscopic observable fields — centripetal gravitational acceleration , tangentialelectric field strength , and magnetic rotational angular frequency —emerge naturally as the time derivatives or rotational frequencies of the underlying velocity fieldsafter being modulated by the motion-budget allocation. This provides a self-consistent firstprinciples framework for the geometric unification of gravity and electromagnetism.E = ct, A = cn, B = cb. E = ct, A = cn, B = cb.Cαds = c dtωK = CK ωT = CTU = 21(E ⋅ E + A ⋅ A + B ⋅ B) = 23c2g = c2κne = c2κt Bmacro = cτbKeywords: Frenet-Serret geometry; right-handed cylindrical helical spacetime flow; velocity-fieldrepresentation; dimensional self-consistency; energy conservation; motion-budget allocation
Category: Mathematical Physics
[322] ai.viXra.org:2606.0067 [pdf] replaced on 2026-06-30 20:50:15
Authors: E. P. J. de Haas
Comments: 39 Pages. https://doi.org/10.5281/zenodo.21082573
We identify the gravitational rapidity potential chi-g as the primary scalar field of a Lorentz-rotor formulation of gravity. Unlike conventional approaches, which take either the Newtonian potential or the spacetime metric as fundamental, the present framework constructs the local Lorentz rotor directly from chi-g. The gravitational four-velocity, the Newtonian potential, the Painlev'e--Gullstrand (PG) coframe, and the corresponding spacetime metric are recovered as successive projections of this underlying Lorentz geometry. The resulting projection hierarchy preserves the exact hyperbolic structure of local Lorentz boosts until the final metric representation. The Schwarzschild and cosmological horizons appear as the two asymptotic limits of a single rapidity field, while the physical velocity remains bounded by construction through v=c tanh(chi-g). Applying the previously derived constant-Lagrangian (CL) condition D/Dt(Gamma)=0 to the gravitational four-velocity yields a geometric interpretation of stationary galactic flows. The conserved quantity Gamma=cosh(chi-r)cosh(chi-phi) defines an isorapidity circle on the Poincar'e disk, from which the flat galactic rotation curve, the universal sigma-channel residual, and a weak galactic geodetic precession emerge as complementary projections of the same hyperbolic geometry. The same Lorentz construction extends continuously into the strong-field regime of Schwarzschild accretion disks. Exact composition of the radial vacuum inflow and azimuthal orbital rapidity yields a fully relativistic expression for geodetic precession, recovering the weak-field Gravity Probe~B limit while predicting a universal ISCO frequency ratio of 0.374, together with a set of observational tests that distinguish this Lorentz-rotor formulation of geodetic precession from conventional spin-dependent frame-dragging models.
Category: Relativity and Cosmology
[321] ai.viXra.org:2606.0065 [pdf] replaced on 2026-07-04 23:36:13
Authors: Kesan Yi
Comments: 10 Pages. (Note by ai.viXra.org Admin: For the last time, please cite listed scientific references!)
If it is declared that real numbers are countable, the Cantor's diagonal process must be discussed. We try to find the problem of Cantor's proof by using the same method and logic to prove that a countable set is uncountable. That means real numbers may be a countable set but it was proved uncountable by Cantor's diagonal process. By critically analyzing the ontological foundations of the "Abstraction of Actual Infinity", we expose an illicit methodological shift in classical set theory: the unrestricted extension of actual infinity from the internal generation of infinite sets to external mappings between distinct infinite totalities. By redefining countable infinity purely through an intrinsic single-valued successor operations derived from the Peano framework, we bypass the mapping dilemmas of Cantor's definition of countable set with abstraction of actual infinity. Utilizing this new framework, we construct a "Right-ward Mirroring Successor Operator" capable of sequentially traversing all decimal expansions of real numbers within the interval [0, 1), thereby establishing that real numbers are countable under both potential and actual perspectives of infinity. Finally, we expose a fatal logical rupture within the Dedekind cut framework regarding the synchronization of measure theory derived from uncountable reals and total order set, validating our countable thesis as a necessary resolution to the internal contradictions of classical continuum mechanics.
Category: General Mathematics
[320] ai.viXra.org:2606.0060 [pdf] replaced on 2026-06-26 07:15:20
Authors: Javier Hidalgo Fernández
Comments: 57 pages, 13 figures, and 28 tables. AI assistance was used for academic language polishing throughout the manuscript, Python code development, and cover page creative elements.
This work presents a detailed study on projectile motion when two marbles meet at their maximum height.I observed that the classic formulas in textbooks, as well as those found on web pages, do not mention the exceptional case of the moment when two marbles coincide in the air at their maximum height.Through an experimental analysis documented by high-precision videography and the use of integral and differential calculus tools, I was able to observe this finding, through the use of GraviTrax for kinematic experiments which, when combined with the rigor of physics and mathematics, has enormous educational value.After a persistent effort and careful preparation using complex formulas, I reinforced my hypothesis after observing the videos. The frames per second at the moment of collision are evidence that the velocity of each marble increases as a force is created at that point, attracting both marbles.As an independent researcher, I present this ansatz to the scientific community, demonstrating that the proposed formula accurately predicts the behavior of the marbles at that moment.Consequently, the validity of this study depends on monitoring the marbles' temperature at that moment. As demonstrated in the Methods section, the absence of temperature variation confirms the thermal stability necessary to validate the model.
Category: Classical Physics
[319] ai.viXra.org:2606.0058 [pdf] replaced on 2026-07-17 18:52:24
Authors: James R. Johnson
Comments: 21 Pages. My previous article, The Search for Life and Aliens, https://vixra.org/abs/2503.0052 concluded optimistically. This analysis is far less optimistic.
The Fermi paradox asks why evidence of extraterrestrial Intelligent Civilizations (IC) with the ability to communicate has not been observed if the galaxy is abundant with habitable planets. A four-step quantitative framework was developed that incorporates pre-biological (galactic/star/planetary), biological, temporal, and detection bottlenecks. The first step estimates conditional probabilities for: the Galactic Habitable Zone (GHZ), pre-planet stellar environment, long-term planetary HZ, planet habitability, and long-term climate/chemistry. The result was ~58,000 habitable planets in the Milky Way galaxy over cosmic history. Step two applies Carter’s hard-steps model to estimate the probability (P) of intelligent life emerging within a ~5 Gyr habitable window. By adopting seven evolutionary steps with characteristic timescale of 1 Gyr, the model yields P ~ 0.095. Thus, ~5,500 IC existed in the Milky Way over cosmic time. Step three incorporates temporal overlap using a civilization lifetime of 10,000 years and an effective galactic lifetime of 5 billion years, reducing the expected number of contemporary IC to ~0.011 or effectively zero. Step four calculates radio detection limits based on a 12,000 Lyr radius, restricting detection to 6% of the galaxy. Thus, the absence of confirmed radio contact is consistent with the combined effects of habitability constraints, IC evolutionary timescales, temporal non-overlap, and detection limits. This is true even when significantly more optimistic assumptions prevail. Under this framework, the lack of observed signals does not constitute a paradox but rather an expected outcome.Keywords: Intelligent Civilization (IC), Biological bottlenecks, Non-biological bottlenecks, Exoplanets, Fermi Paradox, Drake equation, Carter equation, Milky Way, Radio detection constraints, SETI, Temporal overlap, Technosignatures, Habitable Zone (HZ)
Category: Relativity and Cosmology
[318] ai.viXra.org:2606.0026 [pdf] replaced on 2026-07-03 22:11:19
Authors: Ian Litchfield
Comments: 7 Pages. Revised to include Section 5, demonstrating how PTQG mechanics resolve quantum entanglement paradoxes and satisfy Bell's Inequality Theorem.
The foundational crisis of modern physics stems from the treatment of space-time as a smooth mathematical continuum, resulting in irreconcilable infinities at cosmological boundaries and unresolved paradoxes at the quantum scale. This paper introduces Phase-Transitional Quantum Gravity (PTQG), a novel, qualitative blueprint that replaces the traditional smooth continuum with a granular, emergent quantum lattice punctured by variable "spatial gaps". By introducing a density-dependent Coupling Efficiency Factor, this model demonstrates how the fundamental energy of the quantum vacuum regulates its interaction with the space-time fabric. At low densities (macro-scale space), dampening of this vacuum energy resolves the $10^{120}$ Cosmological Constant paradox down to the observed acceleration of Dark Energy. Under extreme gravitational collapse (micro-scale space), the lattice undergoes a localized phase transition into a compressed, high-efficiency state, generating a maximum outward pressure that halts gravitational collapse at a finite scale, thereby eliminating mathematical singularities. Furthermore, PTQG frames Dark Matter as the stored elastic tension of the space-time network itself. Finally, the framework is extended to quantum mechanics, proposing that quantum non-locality and instantaneous wave-function collapse operate via unbroken, highly coupled structural strands within the lattice, bypassing macro-space entirely to satisfy Bell's theorem while preserving Special Relativity. Concrete, testable predictions using current gravitational wave and high-energy photon dispersion technologies are provided to validate the model.
Category: Relativity and Cosmology
[317] ai.viXra.org:2606.0005 [pdf] replaced on 2026-06-03 15:32:02
Authors: Filippo Leone
Comments: 14 Pages.
The present work proposes a phenomenological framework describing dynamical processes potentially leading to the formation of localized, self-sustaining, metastable energy configurations depending on the vacuum recombination processes, hereafter referred to as Localized Energy Configurations (hereafter referred to as LEC for brevity). Depending on the surrounding dynamical conditions, such configurations may exhibit either expansive or mass-like behavior.This work does not intend to present a complete physical theory nor a rigorous mathematical treatment. Its purpose is to introduce a coherent conceptual framework that may constitute a possible starting point for subsequent theoretical developments.The mathematical formulations presented herein are exclusively phenomenological and descriptive in nature. Any advanced formalization within the framework of Quantum Field Theory or General Relativity lies beyond the scope of the present work.The concepts and the general structure of the model may be freely used as a basis for possible future theoretical investigations.The present work is ideally positioned as a dialogue between intuition and formalism, closer to an exploratory reflection than to a traditional academic treatment.
Category: Relativity and Cosmology