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[92] 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
[91] 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
[90] 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
[89] 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
[88] 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
[87] 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
[86] 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
[85] 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
[84] 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
[83] 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
[82] 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
[81] 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
[80] 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
[79] 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
[78] 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
[77] 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
[76] 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
[75] 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
[74] 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
[73] 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
[72] 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
[71] 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
[70] 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
[69] 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
[68] 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
[67] 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
[66] 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
[65] 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
[64] 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
[63] 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
[62] 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
[61] 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
[60] 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
[59] 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
[58] 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
[57] 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
[56] 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
[55] 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
[54] 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
[53] 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
[52] 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
[51] 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
[50] 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
[49] 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
[48] 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
[47] 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
[46] 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
[45] 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
[44] 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
[43] 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
[42] 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
[41] 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
[40] 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
[39] 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
[38] 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
[37] 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
[36] 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
[35] 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
[34] 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
[33] 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
[32] 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
[31] 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
[30] 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
[29] 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
[28] 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
[27] 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
[26] 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
[25] 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
[24] 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
[23] 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
[22] 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
[21] 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
[20] 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
[19] 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
[18] 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
[17] 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
[16] 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
[15] 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
[14] 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
[13] 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
[12] 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
[11] 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
[10] 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
[9] 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
[8] 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
[7] 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
[6] 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
[5] 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
[4] 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
[3] 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
[2] 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
[1] 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