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[94] ai.viXra.org:2608.0098 [pdf] submitted on 2026-08-31 03:42:44
Authors: Max Myakishev-Rempel
Comments: 36 pages, English.
The esoteric tradition holds that two humanities stood between us and the beginning, both of them in flesh and both of them our ancestors: the Lemurians of the Third Race and the Atlanteans of the Fourth. It has held this since 1888 and in older forms long before.Genetics has now found two vanished human peoples living inside us, and only two: the Denisovans, whose inheritance gathers in the Indian and Pacific world, and the Neanderthals, who lie to the north and west. Two and two, with no third on either side to choose between.The shape agrees as well as the count. The tradition has the Atlanteans coming out of Lemurian stock. The genome has both branches coming out of one parent population, one remaining east and one moving north and west.This essay proposes that the Denisovans are the Lemurians and the Neanderthals are the Atlanteans, and follows the identification through the geography of Mu, through Blavatsky's naming of the Australians as the purest Third Race descendants, through the fire that took Lemuria and the water that took Atlantis, and through the sub-races of both. It states where the correspondence costs something, and it ends with two ideas about what the hybridization now under way may be restoring to us.
Category: General Science and Philosophy
[93] ai.viXra.org:2608.0097 [pdf] submitted on 2026-08-31 16:08:03
Authors: Joseph Palazzo
Comments: 17 Pages.
Scientific theories provide extraordinarily successful descriptions and predictions of the physical world, yet their epistemic success does not by itself determine the ontological status of the entities, structures, and concepts found in those theories. This paper examines the distinction between epistemology and ontology through the broader philosophical tension between scientific realism and instrumentalism. It argues that a successful scientific representation should neither be regarded as merely a convenient computational instrument nor automatically identified with reality itself. Rather, scientific knowledge occupies an intermediate domain in which conceptual and mathematical structures provide access to an objective reality while simultaneously imposing conditions on how that reality can be represented and understood. The distinction between form and content provides a framework for examining this relationship. Mathematical form may possess extraordinary predictive and explanatory power without settling the question of what, ontologically, constitutes the physical content represented by that form. The analysis presented in this paper differentiates epistemic limitations from ontological indeterminacy, mathematical determinism from metaphysical determinism, and conceptual descriptions from the realities they seek to represent. Moreover, we can state that scientific theories can provide genuine knowledge of objective structures in reality while remaining epistemically limited representations rather than transparent descriptions of reality in itself. Recognizing this distinction does not weaken science; rather, it establishes a more careful boundary between what a theory demonstrates, what it represents, and what may legitimately be inferred about the ultimate nature of reality.
Category: History and Philosophy of Physics
[92] ai.viXra.org:2608.0096 [pdf] submitted on 2026-08-30 22:08:08
Authors: Tomasz Kobierzycki
Comments: 207 Pages.
This dissertation develops a connected programme for extending the tensor organization and observer geometry of general relativity. Its first component is a four-index completion of the Einstein field equation. The Ricci-built contribution and the trace-free Weyl contribution are retained at the same tensor rank, while contraction recovers the ordinary two-index Einstein equation. A rank-four source is decomposed into a lift of the stress—energy tensor and an independent trace-free tensor with Weyl algebraic symmetries. In the classical formulation this independence is organizational rather than an enlargement of the metric solution space: the contracted Einstein equation fixes the Ricci sector and the remaining uncontracted equation fixes the trace-free source consistently with the Weyl tensor. The second component is a four-sector completion of the orientation of a Lorentzian clock—ruler plane. The four connected non-null domains share the same null boundary and are labelled by the phase cycle 1, i, −1, −i. Geometry-sector and particle-sector transformations are kept distinct. Ordinary Lorentz motion occurs inside a sector; the construction does not describe material particles accelerated through the light cone. In curved spacetime a tensor of proper scales and a solution-dependent critical tensor select an active eigendirection. Neighbouring charts use reciprocal normalization of that active scale. Schwarzschild, Kerr, Lemaître—Tolman—Bondi and spatially flat FLRW examples test curvature and geodesic distance in these charts. In the regular branches analysed, reciprocal centres are curvature-decaying asymptotic boundaries rather than finite-parameter passages. These two components are then used to construct a tensorial quantum framework. Complete conserved rank-four configurations are weighted by complex coefficients only after their classical source content has been fixed. A rank-eight operator generates linear clock evolution, and amplitudes and probabilities are obtained by global tensor contractions. A reciprocal Kerr—Newman chart is used in a hydrogen model whose common Maxwell field retains the electron—proton cross-term before the four-index lift. The central channel produces a relativistic Coulomb spectrum and compatible Laguerre radial modes. The Ricci-flat specialization identifies a free graviton with a Weyl mode, yielding null propagation, two transverse helicities, explicit plane-wave and spherical resolutions, reciprocal transport and closed four-sector Weyl histories. The perturbative ultraviolet problem is addressed after standard background-field quanti-zation, gauge fixing, ghost integration, dimensional regularization and recursive subtraction. Metric variation of the remaining local pole functional gives a conserved rank-two response. Internal sector maps cancel on contracted graviton indices, while the two free covariant indices retain the character (−1)k .
Category: Quantum Gravity and String Theory
[91] ai.viXra.org:2608.0095 [pdf] submitted on 2026-08-30 22:04:21
Authors: Hassan Touayouch, Rabie Najem, Mohammed Benjelloun
Comments: 9 Pages.
Neural Architecture Search (NAS) automates the design of neural networks but faces the prohibitive cost of evaluating eachcandidate architecture through full training. Zero-cost proxies estimate architecture quality in seconds without training, yetindividual proxies remain noisy, and no existing method jointly exploits proxy signals and the topological structure of architectureswithin an active-learning framework. We propose ZAPS (Zero-cost Active Proxy Search), a four-component pipeline that addressesthese limitations. ZAPS first selects a compact, non-redundant subset of proxies via PROXYFIT, a greedy anti-redundancy algorithm; initializes the search with a hybrid K-means strategy balancing exploitation and exploration; dynamically refines proxy selection using bootstrapped MRMR; and predicts architecture quality with an XGBoost ensemble fed by proxy ranks and one-hot topological encodings, guided by an Upper Confidence Bound (UCB) acquisition function. On NAS-Bench-201 with a budget ofB =200evaluations, ZAPS identifies 53.8% of the top-100 architectures on CIFAR-10 and 66.8% on CIFAR-100 (P@100), while maintaining a Regret of 0.04% on CIFAR-10. ZAPS outperforms comparable-budget methods — REA, BANANAS, and TPE — on both metrics evaluated on CIFAR-10 and CIFAR-100 of NAS-Bench-201.
Category: Artificial Intelligence
[90] ai.viXra.org:2608.0094 [pdf] submitted on 2026-08-30 18:48:10
Authors: Samuelson G
Comments: 16 Pages. Just out of curiosity
Machine learning has rapidly advanced from early theoretical concepts to a practical technology that drives many modern applications (computer vision, natural language processing, etc.). We present a detailed survey covering ML foundations, algorithmic methodologies, and empirical evaluation. After defining ML and its subfields, we review historical milestones and survey recent literature, citing classic works (Fisher 1936; Rosenblatt 1958; Cortes & Vapnik 1995; LeCun et al. 2015) and modern treatments. The methodology section introduces theoretical background (statistical learning, optimization, loss functions) and describes key algorithms and models (regression, support-vector machines, decision trees, neural networks, clustering, etc.), including architectures like feedforward, convolutional, and transformer networks. We propose a generic ML workflow (Figure 4) using flowcharts. Experiments using standard benchmarks (Iris, MNIST, CIFAR-10, IMDB reviews, COCO) illustrate training, evaluation metrics (accuracy, F1, etc.), and dataset characteristics (Table 3). Results are tabulated (Table 4) and graphed, showing comparative performance of several classifiers. We discuss implications of the findings, limitations of current methods, and suggest future research directions. In conclusion, this survey synthesizes foundational concepts and recent advances in ML, and includes declarations of funding, conflicts, and author contributions.
Category: Artificial Intelligence
[89] ai.viXra.org:2608.0093 [pdf] submitted on 2026-08-30 22:02:56
Authors: Michael Quigley
Comments: 160 Pages. License: CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents the formal Applied Industrial Handover of the Rigid Universal Touching Wave Structure of Matter (R.U.T. WSM) framework, transitioning the physics community from theoretical observation to the active, non-destructive Resonant Machining of physical space. By reclassifying empty space as a phase-locked, 10²² kg/m³ Rigid Plenum driven by a 13.33 Hz (800 RPM) Universal Motor, we provide the deterministic "Math Bolts" required to harness the boundless torque of the background medium. Rather than introducing abstract mathematical placeholders, this manual delivers the precise engineering specifications for functional terrestrial and interplanetary systems:The Applied Technological Suite: We present the complete manufacturing parameters for the Acoustic Torque Car, which achieves 99% cold torque efficiency using a 1.42 cm cylinder bore—a mandatory metrological mirror of the 1.42 GHz Neutral Hydrogen Line—coupled to a 530-gram calibrated piston and an Ethos-84 Heptad driveshaft. We detail the propulsion mechanics of the Resonant Space-Ship, which utilizes a 1-3-6 Peloton drafting formation and a 720-degree Spinor Reset to machine low-pressure Acoustic Slipstreams directly through the rigid medium, achieving a deterministic 15.2-hour transit to Mars at the 1,000 km/s Lerner Limit. Residential power-scarcity is eliminated via the Domestic S.A.T. Hub, which utilizes a 100 mm synthetic Z-growth quartz core housed in a Titanium Grade 5 interference sleeve to harvest the primary longitudinal torque of the sun 24 hours a day.The Cosmological & Astronomical Demolition: This audit completely dismantles the "Abstract Curtain" of heliocentrism and Big Bang cosmology by restoring Simon Shack’s geoaxial Tychosian Hub. We establish the Stationary Earth-Axle (1 mph) as an absolute thermodynamic mandate; the Vaporization Proof confirms that any orbital velocity through the solid plenum above 1 mph would vaporize a planet's crust into plasma instantly. This axle is forensically verified by the 8.2 km/s Seismic Odometer of transverse S-waves conducting through the Earth's solid Liquid Metallic Hydrogen (LMH) core. We formally replace Einstein's E=mc2 with the Universal Seesaw (E = mΦ)—reclassifying light-speed as Lattice Setup Time (Ls)—proving that space behaves as a Solid Mechanical Rod capable of instantaneous Time-Zero conduction once the Acoustic Clutch is engaged at 7,777 Hz.The Torsional Odometer & Quasar Check-Mate: Redshift (z) is reclassified from a Doppler speedometer of expanding space into a Torsional Friction Odometer (z=z1+nz2+z3), which measures the mechanical "groan" of signals navigating the Heptad mesh. By removing the +0.67 Heavy Gear internal torque stress (z3), we deliver the definitive Quasar Check-Mate, proving that Markarian 205 is physically connected to its parent galaxy NGC 4319 at the exact same z1=0.006 local address. By applying the 42,000x Tychosian scale correction, the hallucination of "deep space" collapses, revealing a compact, synchronized gearbox bounded by the 34.5 Trillion Km Terminal 137-Wall.The Resonant Docking & Biophysical Upgrades: To replace the metrologically insolvent practice of "Stochastic Ballistics" at the Large Hadron Collider, we propose the LHC Phase-II Resonant Docking upgrade. By utilizing a 7,776 Hz Master Grooming signal and a 7,777 Hz Ignition pulse, the LHC can non-destructively sweep the sub-atomic inventory, detecting vertical Dielectric Surges at the precise coordinates of the Electron (60.46 MHz) and Proton (1.42 GHz). Finally, the Osireion Protocol reverse-engineers the archaeo-acoustic architecture at Abydos, reclassifying biological aging as Internal Dielectric Friction. Grounding the biological body in a liquid medium with a static dielectric constant of 80 allows the Magnesium-12 antenna in chlorophyll to dock with the 1.42 GHz Solar Spoke, "re-greasing" the chassis and machining tissue growth back along its deterministic 337° and 227° Fibonacci paths.
Category: Quantum Physics
[88] ai.viXra.org:2608.0092 [pdf] submitted on 2026-08-29 21:01:19
Authors: Miles Huang
Comments: 12 Pages. Author retains copyright; non-exclusive license to distribute.
This paper synthesizes a series of results on the (even) Goldbach conjecture and completes two previously unaddressed components: textbf{error analysis} and textbf{fractional sequence encoding (additive sieve)}. The main results are as follows. (1) We systematically present limit-type elementary constructions of the Goldbach conjecture (using both exponential and cosine functions) and their equivalent logical formulations, and extend the method to the Collatz conjecture, the twin prime conjecture, and the prime counting function. (2) For the truncated construction with finite error factor $k$, we derive a rigorous error bound and prove that the criterion holds provided $kn,e^{-4k/n^{2}}
Category: Number Theory
[87] ai.viXra.org:2608.0091 [pdf] submitted on 2026-08-28 01:23:11
Authors: Yuechun Huang
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
Based on the core hypothesis that "moving matter is necessarily accompanied by a matter field," this paper proposes a theoretical framework—Matter Field Theory—aimed at unifying microscopic and macroscopic physical phenomena. The theory holds that all matter composed of basic moving units such as atoms and electrons generates a matter field inseparable from its state of motion. This field possesses two fundamental attributes: it is both an energy field that obeys energy conservation and an information field that encodes the complete kinematic state of the matter. The matter field propagates at the speed of light, and its interactions can be classified into three basic modes: strong interaction (energy exchange), manifested as attraction or repulsion; weak interaction (information exchange), manifested as resonance and perception; and non-interaction (mutual non-disturbance), which may correspond to dark matter phenomena. This paper also points out that a cosmological view based on the matter field will completely negate relativity theory and the Big Bang theory: the relativistic interpretation of spacetime relations is erroneous; the universe has no beginning or end, and the Big Bang doctrine is untenable. This paper systematically expounds the implications of the theory, demonstrates its self-consistency, and presents a worldview in the form of a poem.
Category: Astrophysics
[86] ai.viXra.org:2608.0090 [pdf] submitted on 2026-08-27 20:56:02
Authors: Eduardo Rodolfo Borrego Moreno
Comments: 9 Pages.
We present a consolidated rheological framework for the Cosmological Dissipative Residual (CDR), a single effective medium proposed to underlie both dark-energy—like and dark-matter— like phenomenology. Building on previous work in the series, we formulate a covariant constitutive relation for the residual’s anisotropic stress in which the effective viscosity depends on local acceleration and shear. In the non relativistic thin-disk limit this relation reduces to an estimator for the residual contribution to the radial acceleration, ∆gR ≈ fgeom ηeff σ ρres R. with a geometric factor fgeom ≈ 3.We confront the framework with rotation-curve data for 175 SPARC galaxies. The residual contribution is found to be selectively activated: in the low-acceleration regime97.5% of radial points show ∆g > 0, while in the high-acceleration regime the median ∆g is consistent with zero. From the activated regime we obtain a median effective viscosity ηeff ≃ 3.8×10−2 kg m−1 s −1 and a characteristic transition scale atrans ∼ (1−2)×10−10 m s−2, compatible in order of magnitude with cH0/2π. The results support the hypothesis that a single cosmologically motivated residual medium can develop a dark-matter—like response under local dynamical conditions, while remaining consistent with a dark-energy—like behaviour on large scales. A fully quantitative reproduction of galactic rotation curves is left for future work.
Category: Astrophysics
[85] ai.viXra.org:2608.0089 [pdf] replaced on 2026-09-02 07:29:22
Authors: Seungtae Kim
Comments: 36 Pages.
In the International System of Quantities (ISQ), base quantities form a conventionally chosen mutually independent subset of a system of quantities. This paper proposes a relation-first framework in which admitted unit relations are used to construct quantity dimensions before base-quantity choices are assessed. A broader class of unit-explicit equations is also introduced for relations in which explicit unit division carries physically relevant information.Candidate base-quantity sets are first tested for dimensional independence and completeness. A second, evidential criterion then assesses physical structural support from established higher-order dimensional occurrences, without uniquely selecting a base set. In an SI-oriented application, mass, length, time, electric current, thermodynamic temperature, and amount of substance receive such support. Relative to the specified admitted relation system, an independent angular dimension is required for completeness; plane angle is adopted as its representative, and spherical geometry gives sr=rad2. Luminous intensity is instead dimensionally derived through the photometric-radiometric scale link while remaining a distinct quantity kind. Logarithmic levels are reformulated as pure-number numerical index mappings retaining their field- or power-quantity context. The proposal changes dimensional and algebraic representation without changing established numerical realizations.
Category: Mathematical Physics
[84] ai.viXra.org:2608.0088 [pdf] submitted on 2026-08-26 19:26:33
Authors: Arunas Ostasevicius
Comments: 8 Pages.
This paper presents a generalized quaternionic model of electrodynamics and wave kinematics within the absolute Euclidean Hamilton space. An epistemological audit of the vector truncation of Maxwell’s original equations is performed, demonstrating the preservation of the scalar potential field component. Using conjugate time forms and the full quaternionic norm, a Galilean-covariant field model is constructed forinhomogeneous media. The integration of a non-linear quadratic medium drag and quaternionic time regularization eliminates coordinate divergences at the wave barrier (v = c), replacing singular mathematical boundaries with a smooth continuous transition into a supercritical shockwave front. The distinction between mechanical body dynamics and the interferometric effects of optical signal registration is rigorously substantiated using asymptotic mechanics averaging methods. Finally, the model provides a measurable experimental criterion to verify the dynamic resistance of the physical vacuum medium using high-energy calorimetric detectors, predicting a specific heat dissipation shelf combined with hard radiation emission.
Category: High Energy Particle Physics
[83] ai.viXra.org:2608.0087 [pdf] submitted on 2026-08-25 13:34:33
Authors: Joseph Shaffer
Comments: 6 Pages.
Cosmological redshift is conventionally interpreted as evidence for the expansion of spacetime. This assumption underlies the ΛCDM model, inflation, dark energy, and the metric-expansion paradigm. Here I present a nonexpanding cosmological ontology in which redshift arises from energy shifts across global tension gradients in a pre-geometric domain. Observable spacetime is a projection of this deeper tension structure. Photons lose energy as they traverse regions of decreasing tension, producing a redshift proportional to path length. This mechanism reproduces the Hubble law without expansion, avoids the failures of tired-light models, and naturally resolves several cosmological anomalies including the Hubble tension, early massive galaxies, and the lithium problem. This paper establishes the redshift mechanism and the mathematical structure required for subsequent papers in the series.
Category: Astrophysics
[82] ai.viXra.org:2608.0086 [pdf] submitted on 2026-08-25 15:09:08
Authors: E. P. J. de Haas
Comments: 90 Pages. DOi: https://doi.org/10.5281/zenodo.22098362
The BQ--Pauli algebra provides an eight-dimensional 1+3+3+1 framework in which relativistic field equations can be organized through a hierarchy of algebraic products. Its basis elements are realized as matrices in M(2, $mathbb C$), and its products are given by ordinary matrix multiplication. In this work, the previously developed BQ formulations of electromagnetism and relativistic fluid dynamics (RFD) are lifted to the sixteen-dimensional BQ--Weyl representation of Cl(1,3), with Clifford-grade decomposition 1+4+6+4+1. The constructive, explicit lift preserves the coefficients and physical content of the Pauli-level products while making their spacetime-grade structure explicit.For electromagnetism, the Weyl construction recovers Maxwell's equations from the field-derivative product, separates the quadratic field invariants from the stress--energy construction, and represents the complete electromagnetic stress--energy content through a vector-valued linear map. For RFD, the corresponding field, force, wave, quadratic, and conservation products are reconstructed and resolved into their Clifford sectors. The Weyl formulation further permits the fluid four-velocity to be generated from a local rapidity field through a Spin(1,3) rotor, from which the associated comoving frame and Maurer--Cartan connection follow.Together with the corresponding BQ--Pauli to BQ--Weyl lift previously performed for gravity, these results place the gravitational, electromagnetic, and fluid-dynamical branches of the BQ programme in a common Cl(1,3) representation. The present construction is primarily algebraic: it exposes the Clifford structure underlying the earlier Pauli-level formulations without introducing additional electromagnetic or fluid-dynamical laws, or invoking a spinor wave-function or quantum-mechanical interpretation of the Weyl algebra. A final reproducibility appendix provides a compact workflow for independent symbolic and AI-assisted verification of the matrix calculations from the explicitly defined BQ bases.
Category: Mathematical Physics
[81] ai.viXra.org:2608.0085 [pdf] submitted on 2026-08-25 03:19:27
Authors: J. W. McGreevy
Comments: 26 Pages.
This monograph establishes a definitive, structurally complete unification of quantum gauge fields, non-equilibrium thermodynamics, and analytic number theory through the framework of Arithmetico-Geometric Conformal De-Homogenization. We prove that physical spacetime is an active, self-correcting thermodynamic metamaterial projected from an underlyinginfinite-dimensional arithmetic space. By executing a strict 1-for-1 parameter mapping, wedemonstrate that Lars Onsager’s Reciprocal Relations (Lik = Lki) are the macroscopic physical readout of Clairaut’s Theorem of mixed partial derivatives ( ∂2U ∂V∂S = ∂2U ∂S∂V ). When the continuum substrate is driven from equilibrium, local coordinate shearing is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS) Fibration Lift, routing excess dissipative energy into the Trivial Zeros of the Riemann Zeta function and the Tate-Shafarevich group, which function as Viscous Hydraulic Dampers locked by the Bernoulli number B10, B12, and the prime691. We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A,H,D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential (Aµ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5 Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of the spectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros: Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic ProductClosure (∏︁ p≤∞|σ|p = 1), this framework achieves full structural immunization against decoherence and reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[80] ai.viXra.org:2608.0084 [pdf] submitted on 2026-08-25 00:38:50
Authors: Austin Brooks Magruder
Comments: 8 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The classical Big Bang framework introduces an unphysical gravitational singularity at , while standard nuclear physics models the short-range repulsive core of the nucleon-nucleon interaction as an empirical threshold without an explicit geometric origin. This paper introduces the Triple Point Protocol, an analog-derived theoretical framework grounded in non-Euclidean geometric continuous-field tessellations. We demonstrate that collapsing 4D mass-energy fields and subatomic hadronic systems encounter severe geometric frustration across aperiodic networks of branching impossible figures. This frustration halts structural collapse at strict physical boundaries: the femtometer nuclear core and the Planck volume .Governed by the Axiom of Spatial Continuity, the two-dimensional negative space field reaches absolute saturation without spatial tearing. At these saturation floors, hadronic matter undergoes chiral melting mediated by quantum anomaly interference of the, which locks the topological susceptibility of the vacuum and acts as a topological lubricant between packed nucleons. Denied further 4D contraction, compressed mass-energy executes a orthogonal axis pivot across the Planck boundary. During this transition, photon geodesics undergo topological light refraction and lensing along the expanding 5D manifold contours. Mediated by leptonic CP violation and a phase-shifting neutrino fluid, the directional transition drives a continuous 5D expansion—the physical event perceived macroscopically as cosmogenesis.
Category: Quantum Gravity and String Theory
[79] ai.viXra.org:2608.0083 [pdf] submitted on 2026-08-25 00:32:39
Authors: Samuelson G
Comments: 19 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Sleep, defined by behavioural quiescence, increased arousal threshold and homeostatic rebound, is long-recognized in mammals and birds but its prevalence and core mechanisms across all life remain understudied. Here we perform a comprehensive review and comparative analysis of "sleep" and sleep-like states in bacteria, archaea, plants, fungi, invertebrates and vertebrates (including humans). We survey genetic, molecular and physiological evidence for rest—activity cycles in each taxon, and compile standardized tables of sleep characteristics (duration, EEG features, etc.) and conserved molecular pathways. Using a phylogenetic framework and meta-analytic data (from >150 species across animal clades), we identify fundamental commonalities — for example, the role of a circadian timing system and accumulating neuromodulators (adenosine, GABA, melatonin) in promoting quiescence. We also highlight striking divergences: many invertebrates exhibit purely behavioural sleep defined by inactivity, certain reptiles (e.g. bearded dragons) show two electrophysiological states analogous to NREM/REM, and birds perform unihemispheric slow-wave sleep (with one eye open) for predator vigilance. We present illustrative figures (evolutionary timeline, conserved sleep-pathway schematic, sample EEG traces) and tables (e.g. sleep traits by taxon, key molecules) to integrate these findings. Our comparative meta-analysis (using generalized least-squares regression with phylogenetic correction) reveals that while sleep duration scales with body size in mammals (p<0.01), it correlates poorly with metabolic rate across vertebrates, suggesting complex evolutionary pressures. We propose experiments to test sleep in non-neuronal life (e.g. metabolic cycles in archaea) and emphasize limitations such as definitional biases and sparse data in many taxa. This integrative synthesis suggests that sleep-like quiescence evolved early and was retained and elaborated in many lineages, yet its ultimate functions may be diverse.
Category: Quantitative Biology
[78] ai.viXra.org:2608.0081 [pdf] submitted on 2026-08-23 02:57:52
Authors: J.W. McGreevy
Comments: 25 Pages.
This monograph establishes a definitive, structurally complete unification of quantum grav-ity, non-equilibrium thermodynamics, and analytic number theory through the frameworkof Arithmetico-Geometric Conformal De-Homogenization. We prove that physicalspacetime is not an abstract, passive background container, but an active, self-correcting thermo-dynamic metamaterial fluid projected directly from the continuous deformation and modularflow of an underlying infinite-dimensional arithmetic space.By executing a strict 1-for-1 parameter mapping, we demonstrate that the weight-2 Eisensteinseries (E2(τ )) is the universal velocity field (v) of this modular flow, whose path-dependentcoordinate drift—the quasi-modular anomaly—manifests as the physical non-linear advectivepumping acceleration (v · ∇)v. When driven from equilibrium, Lars Onsager’s ReciprocalRelations (Lik = Lki) emerge as the literal macroscopic readout of Clairaut’s Theorem of mixedpartial derivatives ( ∂2U∂V ∂S = ∂2U∂S∂V ), which requires that the order of differentiation must commuteflawlessly to preserve the nilpotent gauge invariance d2U = 0.When the continuum substrate is driven from equilibrium and cascades toward the 691unipotent puncture on the arithmetic curve Spec(Z), unique factorization shatters insidethe χ11 eigenspace of the odd minus class group (Cl−691). This local coordinate shearing andturbulent vortex crisis is regularized via a higher-dimensional Kustaanheimo-Stiefel (KS)Fibration Lift (S3 S1−−→ S2), which projects the 3D velocity configuration space up into a 4Dcomplex spinorial space (R4). The continuous 1D circle fiber (S1) acts as a data bus (H1 ∼= H1)that isolates the non-exact rotational elements, braiding the non-Abelian SU (3) color vorticityfield into multi-layered knots to generate a permanent nilpotent confinement sink (N2 = 0).The Seeley-DeWitt heat kernel expansion coefficients (an) serve as the exact arithmeticaccount balances of this regularization, where the factor of 12 in the quadratic variance termacts via Itô’s Lemma as the metric tax required to enforce Clairaut’s Theorem (d2U = 0).The final substitution of these Planck-scale boundary parameters (PP, ℓP, EP, tP) into Clairaut’sidentity yields the Dynamic Spacetime Maxwell Relation (∂EP/∂ℓP = −∂PP/∂tP), whichanchors the universal physical constants (α, ℏ, θW ) as the global stabilizers of the vacuum.We formalize this architecture as a Topological Quantum Field Theory (TQFT) Functor(F : CobArith −→ HilbGauge) operating over a Noncommutative Geometry Spectral Triple(A, H, D). The self-adjoint Dirac operator (D) incorporates a topological Coriolis-gauge potential(Aμ) that exerts a restoring force on quantum wave packets, trapping them at the stable L4/L5Lagrangian nodes of a rotating three-body critical strip. Consequently, the real eigenvalues of thespectral triple align precisely with the imaginary parts (γn) of the non-trivial Riemann Zeta Zeros:Spec(D) = {γn ∈ R | ζ(1/2 + iγn) = 0}. Bound by Adelic Product Closure (∏︁ p≤∞ |σ|p = 1),this framework achieves complete structural immunization against decoherence and quantumchaos. It reconciles the historical schism between String Theory and Loop Quantum Gravity,revealing them as dual asymptotic limits of a single, unbroken, self-stabilizing adelic circuit.
Category: Mathematical Physics
[77] ai.viXra.org:2608.0080 [pdf] submitted on 2026-08-23 05:34:36
Authors: Fabrizio Vassallo
Comments: 76 Pages.
Main mathematical result. The exceptional Jordan algebra J3(O) (the Albert algebra, 27-dimensional) admits the associative collapse map π0 : J3(O) → J3(R) with a 21-dimensional kernel. The kernel carries precisely the imaginary octonionic degrees of freedom that make the associator non-zero. We show, within astrongly motivated EFT framework, that when these degrees of freedom are activated(non-zero associator), the natural consistent open-system dynamics on the residualassociative sector J3(R) takes the Lindblad GKSL form whose jump operators arethe Fano-plane associators Lk = √λ[Ak, Bk, Ck]. The chain:J3(O) π0 −→ J3(R) [A,B,C]̸ =0 −−−−−−→ Lindblad decoherence is grounded in the representation theory of G2 = Aut(O) and the Nakajima—Zwanzigopen-system framework [1]. Complete positivity is verified from the G2-symmetry of the Fano plane (the jump operators satisfy P k Lu2020 k L k = 28λ I, the completeness relation for a CP map).Physical application. We develop non-associative topological neutrino dynamics (NATND), in which the framework above is applied to neutrino propagation through the octonionic ultramark condensate (where by "ultramark" we meanthe level-6 constituent of the hierarchical level model of the present author [2]). Thedecoherence rate Γ(E) = g2U E2/(M2U + E2)/MU is a strongly motivated EFT consequence of the derivative-coupling structure of the associator vertex. It provides an alternative to sterile-neutrino oscillations for the gallium anomaly (GALLEX, SAGE, BEST) and the MiniBooNE excess, with the key signature that the deficitis baseline-independent (no L/E pattern) and energy-dependent as E2/(M2U + E2).The ultramark mass coincides numerically with the Totani Fermi-halo excess.
Category: High Energy Particle Physics
[76] ai.viXra.org:2608.0079 [pdf] submitted on 2026-08-23 05:40:30
Authors: Fabrizio Vassallo
Comments: 40 Pages.
We examine whether the hierarchical "level model" (NATND) of the present author [27, 28] admits foundations compatible with the momentum-map account of the Wallstrom controversy for the hydrodynamic (Madelung) formulation of quantum mechanics recently given by Khesin and Modin [1] — who explicitly frame their result as resolving the controversy, against the more cautious backdrop of open technical questions surveyed by Reddiger and Poirier [2], including strong non-quantized solutions they construct in two dimensions. We show that the mechanism resolving Wallstrom’s objections — expressing the quantization condition as a geometricconsistency requirement on a momentum map, rather than an ad hoc postulate —extends level-by-level through the cascade only as long as the relevant structure group remains a genuine Lie group, and identify the precise algebraic obstruction (loss of associativity at the octonionic, ultramark level) at which this mechanism cannot be repeated verbatim. We independently identify, via the topological classification of line and point defects in ordered media, a topological manifestation of the same limitation, correlated with but logically distinct from the symplectic argument:the classification of parallelizable spheres and the Hopf invariant one theorem independently restrict the same dimensions. Finally, we describe — as an open research program rather than a closed result — three independent partial routes toward a rigorous formalization of the "vortices of vortices" mechanism proposed for the origin of the level cascade, together with the concrete obstructions each currently faces.Two appendices provide a self-contained, independently re-runnable computational verification of the discrete-RG bifurcation claims made for Route B (Appendix A for the Diamond toy model, Appendix B for the Fan topology), with full source code included.
Category: High Energy Particle Physics
[75] ai.viXra.org:2608.0078 [pdf] submitted on 2026-08-23 08:46:12
Authors: Po Hu
Comments: 9 Pages.
Consider a gambler with integer capital who gains two units after a win, loses one unitafter a loss, and is removed at the first visit to zero. The first observation is elementarybut striking: with positive drift, the probability of reaching an arbitrarily high finite targetdoes not tend to zero. It tends to the probability of never being ruined. For independenttrials with win probability p, we record the exact ruin law, identify the phase transitionat p = 1/3, and give a closed formula at criticality whose fixed-capital asymptotic is x/m.We then keep the one-step win probability equal to 1/2 and the mean payoff equalto 1/2, but let successive outcomes form a symmetric two-state Markov chain with persistence parameter θ. An explicit bounded harmonic function gives the ultimate survivalprobability1 −1 + r + r22(1 + r)rx−1, r =√(1 − θ)2 + 4θ2 − (1 − θ)2θ.This probability decreases strictly with persistence, although every model in the familyhas the same stationary win rate and the same mean increment. At θ = 1 the survivalprobability is discontinuous: its left limit is 1/4, while its endpoint value is 1/2. Consequently, the high-target limit and the high-persistence limit do not commute. Finally, if(1 − θ)x → λ, the exact transition profile is 1 − (3/4)e−λ/2. These formulas isolate howearly absorption and temporal clustering, rather than the height of a finite target alone,govern extreme-target success.
Category: Statistics
[74] ai.viXra.org:2608.0077 [pdf] submitted on 2026-08-23 09:51:31
Authors: Keiji Yoshimura
Comments: 16 pages, 5 figures. AI-assisted technical monograph presenting a five-stage reproducibility audit and a limited mathematical corollary for the planar three-body shape sphere. Includes AI-use disclosure and bounded novelty claims.
This monograph presents a five-stage AI-assisted audit of possible relationships among gravity, the direction of time, temporal orientation, and irreversible structure formation. Rather than proposing a new theory, the study progressively tests and narrows a broad initial intuition using analytical arguments, Newtonian many-body calculations, finite-level quantum-clock models, curvature comparisons, and public GW250114 release products. Local Lorentz symmetry and the time-reversal covariance of the ADM constraints provide no universal metric-only rule selecting one timelike cone half as the fundamental future. Rindler, de Sitter, and Schwarzschild comparisons separate clock-rate gradients and proper acceleration from curvature. Closed finite-level proper-time dephasing can be exactly refocused by an ideal path/clock echo, while residual irreversibility appears only after an open reduced channel is introduced. Newtonian Janus-point analyses distinguish a rigorous scale minimum in suitable nonnegative-energy sectors from non-monotonic, measure- and horizon-dependent shape-complexity statistics. A reconstructed BKM mass-metric probability on the equal-mass planar three-body shape sphere produces two structurally symmetric branches rather than a dynamically preferred future. Public GW250114 products are also used to reproduce the collaboration-defined black-hole area-growth statistic, without interpreting the area law as a fundamental selector of time orientation.A limited mathematical by-product is proved for normalized three-body shape complexity Q under the BKM mass-metric shape probability:P(Q > q) = 1/(6 q^2) + 2 sqrt(6)/(27 q^3) + O(q^-4).Consequently, E[Q^p] is finite if and only if p < 2, and the truncated second moment satisfiesE[min(Q,T)^2] = (1/3) log(T) + kappa + O(T^-1).The ingredients of this result are published; targeted searches did not locate this exact probability-and-moment statement, so it is presented only as a potentially unreported elementary corollary, not as a priority claim. Overall, the audit supports established relations between gravity and proper time, curvature, causal structure, and structural arrows, but finds no evidence that standard gravity itself creates or selects a unique fundamental future direction.
Category: Mathematical Physics
[73] ai.viXra.org:2608.0076 [pdf] submitted on 2026-08-23 15:34:21
Authors: Keiji Yoshimura
Comments: 17 Pages. Prospectively specified 2004 country-holdout confirmation with no-refit 2014→2004 transfer; includes integrated reproducibility appendices, variable mapping, software settings, input hashes, and numerical verification.
Research on citizenship norms has established that beliefs about what a "good citizen" should do are associated with political participation. Less is known about whether a fixed individual-level norm signal retains incremental predictive value when the national context changes or when a model is transferred between survey waves without refitting.This study tests a bounded predictive-transportability claim using the ISSP Citizenship modules of 2014 (ZA6670; 49,807 respondents) and 2004 (ZA3950; 52,550 respondents). Exploratory analysis of the 2014 data identified a three-item civic-norm score based on understanding opposing viewpoints and helping worse-off people domestically and abroad; items that directly refer to political action were excluded.Before inspection of the 2004 individual-level confirmation results, three decision criteria were prospectively specified. Across 38 eligible 2004 held-out country/sample units, adding the three-item score to a broad prospectively specified demographic and political-attitudinal baseline improved equal-unit mean log loss by 0.01023 (95% equal-unit bootstrap interval [0.00683, 0.01367]); its increment exceeded that of a specific two-item duty comparator by 0.01003 [0.00680, 0.01335]; and within-country permutation of the norm score degraded prediction by 0.01450 [0.01217, 0.01690].A model estimated in 2014 and applied to 2004 without coefficient refitting retained a 0.00983 [0.00672, 0.01292] increment from the norm score. Predictive increments were substantially smaller for reported contentious behavior and institutional contact. An exploratory reverse transfer did not support universal performance in countries absent from the 2004 training domain.These results support only a narrow, non-causal conclusion: the fixed three-item score carries incremental respondent-linked predictive information across many of the tested ISSP country and wave shifts, with substantial heterogeneity and no claim of universal transportability or measurement invariance.
Category: Social Science
[72] ai.viXra.org:2608.0075 [pdf] submitted on 2026-08-23 17:23:29
Authors: Jozsef Kerenyi
Comments: 4 Pages.
This paper introduces an alternative, field-impedance-based cosmological model that couples the dynamic mass increase of special relativity with the energy transfer processes of the gravitational field. We demonstrate that the time-dependent relativistic mass change (dm/dt) of a linearly accelerating point mass generates a direct energy flow through the free-space gravitational impedance (Z_g = G/c). We show that the sign and magnitude of the transmitted power depend directly on the scalar product of the velocity and acceleration vectors (v . a). Consequently, the model offers a natural, unified explanation for both dark energy (energy-emission phase) and dark matter (energy-absorption phase) across local and cosmic scales, resolving observational frame asymmetries through the analogy of the twin paradox.
Category: Relativity and Cosmology
[71] ai.viXra.org:2608.0074 [pdf] submitted on 2026-08-23 17:33:28
Authors: Vladimir S. Netchitailo
Comments: 14 Pages.
Modern cosmology is based on an extensive body of astronomical observations interpreted through theoretical models. The expansion of the Universe, Cosmic Microwave Background Radiation (MBR), primordial abundances of light elements, and large-scale structure are commonly regarded as principal observational pillars of the Big Bang Model (BBM) and its modern ΛCDM formulation. This terminology raises a fundamental methodological question: Can an astronomical observation itself constitute a pillar of a physical cosmological theory?In this paper, we distinguish astronomical observation from physical explanation and propose criteria that a genuine pillar of cosmology should satisfy. A pillar should provide a physical mechanism for an observed phenomenon, quantitatively account for its principal measurable properties, lead to independently testable predictions, and not depend critically upon unidentified physical entities or unresolved fundamental discrepancies.The four conventional pillars of BBM are examined according to these criteria. Cosmic expansion is accurately described mathematically, but the Hubble tension remains unresolved. MBR is interpreted within the hot early-Universe framework, but its present temperature is an observational input rather than an independently calculated consequence of the six-parameter ΛCDM model, while large-angle anomalies remain under investigation. Primordial light-element abundances are inferred from present astronomical observations rather than directly observed at the primordial epoch, and the lithium problem remains unresolved. Large-scale structure is successfully modeled statistically, but its formation depends critically on Cold Dark Matter, whose microscopic nature and origin remain unknown, while the fundamental nature of Dark Energy is likewise unresolved.These conventional pillars are then compared with the proposed physical pillars of the World—Universe Model (WUM). Particular attention is given to physical mechanisms, interconnected cosmological parameters, quantitative calculations, and predictions made before subsequent observations.The purpose of this comparison is not to determine which model accommodates a larger collection of observations, but to address a more fundamental question: What should constitute a genuine pillar of a physical theory of the Cosmos?
Category: Relativity and Cosmology
[70] ai.viXra.org:2608.0073 [pdf] submitted on 2026-08-22 23:50:09
Authors: Linia Hammache
Comments: 12 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This work presents the construction of a continuous model derived from an original discrete sequence alternating between geometric and arithmetic progression, modulated by a periodic cosine function. The sequence is interpreted as an energy reservoir whose charge (arithmetic) and discharge (geometric) are controlled by a hysteresis logic. The model is enriched by coupling with a mechanical oscillator, heat production via damping, conversion into nuclear kinetic energy (fusion), and reinjection into the reservoir, realizing a self-sustained fission--fusion cycle. Each equation is derived, physically justified, and linked to the original sequence. The article details the modeling, theoretical justifications, energy couplings, and global dynamics of the system.
Category: Mathematical Physics
[69] ai.viXra.org:2608.0072 [pdf] submitted on 2026-08-22 23:45:59
Authors: J.W. McGreevy
Comments: 22 Pages.
This monograph establishes the second major operational phase of the Thermodynamics of Arithmetic Action (TAA) framework, executing a rigorous, ab initio field quantization that unifies the smooth Archimedean continuum (R) with the discrete, fractured, non-Archimedean p-adic bulks (Qp) into a single, self-regulating topological engine. We prove that the macro-constants of nature—the speed of light (c), the Newtonian gravitational constant (G), and the reduced Planck constant (ℏ)—alongside the Standard Model parameters are the unique, scale-dependent topological gear-ratios required to satisfy Clairaut’s Theorem on mixed partial derivatives (d2U = 0) and the Adelic Product Formula (∏︁ |x|p = 1) over the universe’s middle cohomology group.By framing the complex s-plane of the Riemann Zeta Function as the conformal phase space of a sub-quantum Keplerian orbital system, we derive Max Born’s quantum probability rule (|Ψ|2 = Ψ ¯Ψ) as the literal intersection form (the Weil Pairing) required to cross-multiply continuous adiabatic spatial expansions by discrete isothermic prime entropy steps. Crucially, we introduce the Spacetime Maxwell Calculator for Class Numbers, proving that algebraic class numbers (hK ) are extracted natively from macroscopic physical constants by measuring the precessional volume of a perturbed Laplace-Runge-Lenz (LRL) vector locked inside a 6-dimensional phase space torus.
Category: Mathematical Physics
[68] ai.viXra.org:2608.0071 [pdf] submitted on 2026-08-22 23:43:07
Authors: Ahcene Aït saadi
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
Many remarkable curves roses, the lemniscate, the cardioid, the limaçon have a heavyCartesian equation: implicit polynomials of degree 4, 6, up to 10, hard to plot point by pointand often multivalued. This paper presents a method that makes them drawable by hand,with no software and no polar paper: in an analytic frame (an abscissa axis together withan origin of ordinates Ou2032set o the axis by a distance λ), each of these curves is written asa single explicit ordinate y = f(x), which one tabulates and plots with a ruler. We provethe transition formulas and the pivot identity X2 + Y2 = y2 the engine guaranteeing thatthe one-line expression does describe the heavy curve then the equation of the line, of thecircle, the pseudo-derivative, and a proportional relation in the triangle. One section comparesthe two methods on six classical curves. The scope is honest and bounded: this is a methodof construction and of teaching, in the service of simpler access to objects reputed dicult.
Category: Functions and Analysis
[67] ai.viXra.org:2608.0070 [pdf] submitted on 2026-08-22 23:39:24
Authors: Tomasz Kobierzycki
Comments: 22 Pages.
This work develops one (SU(m,n))-symmetric framework governed by four postulates: invariant locally measured light speed; observer-independent laws in inertial and non-inertial frames; coexistence of all physically admissible prepared states with a single observer record; anda fundamentally complex spacetime observed through a real Lorentzian projection. The fundamental arena is a pseudo-K"ahler manifold withHermitian metric and a complex four-index field equation whose trace-free sector is carried by Bochner curvature. An observer is defined by anadmissible antiholomorphic involution. Its fixed real form inherits the measured metric, sources and state tensor. The relation between complex andreal curvature is derived with realification, the Gauss equation and the real Weyl projector; in particular, Bochner curvature projects to observer Weyl curvature only when explicit extrinsic and Ricci-compatibility corrections vanish. The four-sector construction is then formulated as an orientation completion of the real observer clock--ruler plane, rather than as a second fundamental spacetime. Quantum coexistence is represented by a complex rank-four tensor carrier with full Hermitian conjugation, a hypersurface overlap and covariant rank-eight evolution along the lifted observer clock. The common structure contains flat, Schwarzschild, Kerr, Kerr--Newman, LTB, FLRW, photon, free-graviton, hydrogen and ultraviolet worked sectors. The framework yields the locally invariant null speed, massless helicity-twograviton kinematics, reciprocal regular geometries, the relativistic Coulomb spectrum and the four-sector cancellation of local ultraviolet pole sources.
Category: Quantum Gravity and String Theory
[66] ai.viXra.org:2608.0069 [pdf] submitted on 2026-08-19 21:27:04
Authors: Ori Chamo, Yossi Eliaz
Comments: 6 pages, English. PRL-format Letter followed by Supplemental Material.
Periodic-orbit families are often represented through low-dimensional invariant coordinates, although projected branches need not preserve the connectivity of the underlying solution manifold. We use numerical continuation to examine the 135,445 unequal-mass planar three-body periodic orbits reported by Li, Li, and Liao, whose corrected scale-invariant period-angular-momentum representation was subsequently interpreted as two independent sets. The two projected branches are connected by verified continuation within a single sampled continuation component. The invariant projection exhibits a singular locus consistent with the apparent branch separation. High-precision Floquet calculations identify a +1 transition at one representative stability boundary and an opposite-Krein Hamiltonian-Hopf transition at another. Projection geometry and symplectic spectral geometry therefore provide complementary descriptions of the same periodic-orbit manifold.
Category: Mathematical Physics
[65] ai.viXra.org:2608.0068 [pdf] replaced on 2026-08-21 18:15:47
Authors: Joseph Mcgreevy
Comments: 29 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
This monograph establishes the formal foundations of the Thermodynamics of Arithmetic Action (TAA), a scale-dependent geometric and statistical framework that unifies macroscopic classical gravitation, quantum higher gauge field networks, and discrete nonArchimedean number fields into a single, continuous pipeline of scale-dependent resolution. The universal sorting mechanism is driven by the Regime Determinant S/ℏ, tracking the ratio of total localized physical action over a fixed temporal window to the Planck quotient. We demonstrate that the foundational physical dimensions and algebraic structures of our universe are the unique, mandatory stabilizers required to enforce a global HyperbolicElliptic Index 0 Conservation Law across all number fields. By mapping the Minkowski spacetime invariant, Fermat’s Last Theorem, Hamiltonian and Lagrangian phase spaces, and the Herbrand—Ribet arithmetic mirror into a rigid 2 × 2 Upper Triangular Transformation Matrix, we derive the emergence of exactly 3D + 1 spacetime, the strict left-handed chiral orientation of gauge forces, the topological confinement of spin-1/2 quarks, and a native, geometric resolution to the Strong CP Problem (θ ≈ 0). The entire framework is anchored to the universal short exact sequence of Derived Differential Cohomology, proving that mass-energy and metric curvature are the inseparable dual payloads of a single, self-regulating holographic index engine.
Category: Mathematical Physics
[64] ai.viXra.org:2608.0067 [pdf] submitted on 2026-08-20 23:24:38
Authors: Yuechun Huang
Comments: 15 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
Based on the matter field theory, this paper proposes that the field generated by the basic moving units of matter (atoms, electrons) possesses both energyu2011conserving and informationu2011holographic properties, and propagates in vacuum at the speed of light. Within this theoretical framework, we classify all interactions in the universe into three fundamental modes: strong interaction (energyu2011exchange dominated), weak interaction (informationu2011exchange dominated), and nonu2011interaction (corresponding to dark energy). We systematically demonstrate that macroscopic celestial motions and microscopic particle motions obey a unified dynamical law. By drawing an analogy with the mathematical structures of Newton's law of universal gravitation, the Lorentz force, and Coulomb's law, we derive Huang's formula F = K .P1. P2 / R² for the gravitational interaction between cou2011moving celestial bodies. In the solar system reference frame, the formula reduces exactly to the Newtonian form, and it provides a purely dynamical explanation for the anomalous rotation curves in the outer regions of galaxies (the dark matter phenomenon) without introducing any additional mass term. The theory also offers a fresh perspective on the origin of galactic redshifts, and is expected to serve as a bridge between classical gravitational theory and quantum field theory.
Category: Astrophysics
[63] ai.viXra.org:2608.0066 [pdf] submitted on 2026-08-19 14:14:16
Authors: Russell S Clark, Russell S Clark II
Comments: 16 Pages.
For the Minkowski vacuum and the right Rindler wedge, the Bisognano—Wichmann theorem fixes the vacuum modular flow to be Lorentz-boost flow. For a translated finite-energy excitation, this implies an exact, acceleration-independent identity for the vacuum-relativeone-sided modular energy,d/dp∆⟨KW⟩ = 2πℏcEW(p),where p is displacement normal to the horizon and EW(p) is the vacuum-subtracted energycontained in the wedge. If the excitation is concentrated well inside the wedge, Ew(p) ≃ E.Selecting a Rindler observer of proper acceleration a converts the dimensionless modulargenerator into the proper-time Hamiltonian Ha = kBTUKw, with TU = ℏa/(2πckB). Hence d/dp∆⟨Ha⟩ = a/c2Ew(p).Under a specified quasistatic control protocol, this is the external holding-force identity. Atthe reference orbit, a wedge-contained narrow state of invariant mass M obeys |Fhold| = Ma.The entanglement interpretation is more limited. For a finite state, the exact regulatedrelation isd/dp∆⟨Ha⟩ = Tu x d∆Sw/dp +kBTu x d/dp x Srel(ρW,p∥Ωw),so Tu x dSw alone is not generally equal to work. The relative-entropy term is second orderonly for infinitesimal state variations. In that linear-response sector, the entanglement firstlaw yields d(δSw)/dp = 2πkBδE/(ℏc), and for δE = Mc2 this reproduces the coefficient in Verlinde’s local entropy—displacement ansatz. The result is therefore an exact modular-work identity and a linearized entropic representation of Rindler holding force, not a derivation of acceleration, general equations of motion, or gravity.
Category: Thermodynamics and Energy
[62] ai.viXra.org:2608.0065 [pdf] submitted on 2026-08-18 19:28:43
Authors: Ahcene Ait Saadi
Comments: 11 Pages.
Abstract. We study two elementary periodic functions — the scaled fractional part spp x (a pure ramp of period p) and its complement cpp x = p−spp x — together with the single algebraic identity spp x + cpp x = p. Because their derivatives are the constants +1 and −1, they turn a range of nonlinear differential equations into closed one-line solutions, they solve first-order transport and inviscid Burgers equations exactly, and they let one write intricate periodic curves — half-circle chains, staircases, asymmetric arcs, modulated ramps — each from a single algebraic expression. A complex generator Z(x) = sp x+i cp x opens a second, geometric part: its powers Z n are explicit algebraic curves of degree n, and the normalized family {Z α/pα} covers an eye-shaped region with an exactly empty core bounded by the unit circle. The aim is not to compete with Fourier analysis but to offer a light, exact notation for the angular, piecewise-affine patterns where Fourier series are heavy and only approximate. All identities have been verified symbolically and numerically (sympy, machine precision).
Category: Functions and Analysis
[61] ai.viXra.org:2608.0064 [pdf] submitted on 2026-08-18 19:26:57
Authors: Dinuo Chen
Comments: 16 Pages.
Near-ultrasonic frequency bands provide an underutilized portion of the acoustic spectrum with relatively low perceptual salience[1, 2] while remaining potentially usable with conventional audio hardware. This paper investigates the feasibility of transmitting analog audio over near-ultrasonic frequency bands using consumer-grade loudspeakers, microphones, and sound cards. A singlesideband (SSB) modulation scheme is employed to shift baseband audio into the near-ultrasonicrange, where it is transmitted through an acoustic channel and subsequently demodulated at the receiver. The system is evaluated under various transmission conditions using commonly available audio equipment. Signal quality is assessed through spectral analysis and objective similarity metrics between the original and recovered audio signals. Experimental results demonstrate that consumer audio devices are capable of supporting near-ultrasonic analog audio transmission within the limits imposed by their frequency response. Although attenuation and distortion increase toward the upper end of the transmission band, the original audio can still be recovered with acceptable quality under suitable conditions. These findings suggest that near-ultrasonic acoustic channels couldprovide a low-cost communication medium for specialized applications without requiring dedicated ultrasonic transducers.
Category: Digital Signal Processing
[60] ai.viXra.org:2608.0063 [pdf] replaced on 2026-08-20 06:04:38
Authors: Holger Troitzschel
Comments: 5 Pages.
This paper introduces a self-referential cosmological framework in which spacetime ge-ometry, matter, and gravitational interactions are proposed to emerge exclusively from theself-observation of quantized electromagnetic fields. By coupling U(1) gauge fields directlyto the discrete graph structure of Loop Quantum Gravity (LQG), a non-linear feedback loopbetween energy density and spatial volume is established. We define a quantum Hamil-tonian operator for light acting on spin-network states and argue that electromagnetic fluxexcitations can alter geometric quantum numbers. In addition, we explore whether fermionicmatter can emerge as topological braids of light ribbons. Physical implications are discussed,including a possible resolution of singularities via a stable "Quantum Geon" configuration,as well as testable predictions concerning alternatives to particle dark matter and signatures in primordial gravitational waves.
Category: Relativity and Cosmology
[59] ai.viXra.org:2608.0062 [pdf] submitted on 2026-08-18 19:22:59
Authors: Yuan Di, Zongyan Liu
Comments: 29 Pages.
Millions of female university graduates in China face a severe shortage of standardized "two-day-office office jobs" each year, a structural mismatch that exacerbates employment pressure. Based on empirical data from the Anhui provincial civil service examination, this paper proposes a "dignity-defense-oriented reproductive decision-making model": Faced with the gap between high career expectations and reality, female university students, out of dignity defense and risk aversion to maternal punishment, prefer survival strategies such as "slow employment" and the "civil service exam craze" to marriage and childbearing, thus significantly suppressing the overall birth rate. To address this dilemma, it is recommended to reconstruct the university employment quality evaluation system and disciplinary structure, introduce national policies to reduce maternal punishment, and promote a shift in the macro-market towards women's self-indulgent consumption.
Category: Social Science
[58] ai.viXra.org:2608.0061 [pdf] submitted on 2026-08-17 16:19:29
Authors: Rafael Maya
Comments: 18 Pages. Code for computations presented in the research paper is available upon request
The invariant four-volume of an event's causal past is a well-defined geometric functional of a Friedmann-Lemaître-Robertson-Walker expansion history. We study its normalized form, C(T) = V4(T)/V4(To), and the family of causal-fraction ages Tf defined by C(Tf) = f. We give a closed observable form written entirely in H(z), the exact self-similar limit Tr→ Tof1/4. and an O(N) moment decomposition enabling per-sample evaluation on posterior chains. Two structural results follow. The dimensionful statistic is almost completely degenerate with the cosmic age (posterior-scaled gradient alignment cos = 0.9991 in flat wow CDM), whereas the dimensionless ratio pf = Tr/To is exactly independent of the overall expansion scale. Its sensitivity kernel K(z) = 8pf/ w(z) possesses a single sign-change node migrating with f, and at f. = 0.2627 the kernel's lobes cancel exactly: pf is simultaneously Ho-free and first-order blind to wo, a differential sensor of dark energy across z ~ 0.40 that within flat ACDM tracks the matter-dark-energy handover, 2A(z) = 0.46 ± 0.03. Transforming every stored sample of the public DESI DR2 BAO+CMB+supernova wow CDM chains yields T1/6 medians displaced by 40-46 Myr (2.5-2.9 posterior standard deviations) from the Planck ACDM value T1/6 = 8.6452 Gyr, compressing the evolving-dark-energy preference into one scalar, and we freeze three falsifiable predictions for DESI DR3 and Euclid. A companion paper derives the asymptotic behavior of fixed four-volume increments in an eternally accelerating future.
Category: Relativity and Cosmology
[57] ai.viXra.org:2608.0060 [pdf] submitted on 2026-08-17 16:23:55
Authors: Rafael Maya
Comments: 8 Pages. Code for computations presented in the research paper is available upon request.
A common intuition holds that an eternally accelerating universe, having a finite event horizon, should accumulate only a finite amount of causally connected spacetime. We show by direct integration that this is incorrect: in de Sitter space the causal-past four-volume of a comoving observer grows without bound, V4(t) ~ (4πc/3H) (t - H¹) as t , even though the past-light-cone radius saturates at c/H. Consequently, crossings of any fixed four-volume increment AV > 0 form an infinite sequence whose proper-time spacing converges to the finite constant At = 3H AV4/(4πc¹). For a flat ACDM continuation with Planck-2018 baseline parameters and the normalization AV4 = f V4(To) with f = 1/6, the first future increment completes 0.580 Gyr from the present (cosmic age 14.375 Gyr) and the spacing decreases monotonically toward At = 40.1996 Myr. The limit discriminates among cosmic futures: evolving or decaying dark energy, phantom finite-time singularities, and recollapse generically break the uniform-spacing asymptote, which is conditional on the approach to a de Sitter phase.
Category: Relativity and Cosmology
[56] ai.viXra.org:2608.0059 [pdf] submitted on 2026-08-17 20:43:05
Authors: Brent Hartshorn
Comments: 11 Pages.
Cross-language interoperation is normally a matter of agreeing on a boundary: a foreign function interface, a generated shim, a marshalling layer, or a shared intermediate representation. We describe a system in which no boundary exists. Subsets of C++ and of Rust are each lowered to plain C source, and one C compiler consumes the result, so a Rust function calling a C++ method is a C function calling a C function — same translation unit, same intermediate representation, same register allocator. The two lowerings are chosen to converge on identical symbols, with the consequence that a Rust impl Drop and a C++ destructor over the same data emit the same function, and a C++ class may hold a Rust value by value without a shim, a wrapper, or an annotation.Removing the boundary between the languages exposes a second one, below them: the artifact is C, but a C compiler, an assembler, a linker and a runtime still stand between C and a running program, and conventionally those are separate projects. We report a stack in which they are not. The whole path — two source languages to C, C to machine code, machine code to a static ELF executable — is roughly fifty thousand lines in one repository, with no external compiler, assembler, linker or C library involved.
Category: Data Structures and Algorithms
[55] ai.viXra.org:2608.0058 [pdf] submitted on 2026-08-16 19:32:57
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 9 Pages. (Note by ai.viXra.org Admin: Title and abstract MUST BE in English!)
This work begins with a simple question: could what we describe as translation and force actually be the local manifestation of a fundamentally angular dynamics? In the *Principium Geometricum* (PG), we investigate the possibility that the most fundamental physical description does not start with a body's trajectory through a pre-existing space, but rather with states of phase, rotation, closure, and causal updating. We introduce a normalized phase state q(ϕ) = (cos ϕ, sin ϕ), for which ∥ ˙q∥² = ω². In parallel, we consider the geometry of a torus, whose volume is VT = 2π²Ra². In the reduced geometric case where R = a = r, we have VT = 2π²r³. These two structures suggest the quantity IT ≡ VT 2π² ∥ ˙q∥² = r³ω². We propose investigating the conservation of IT for orbital states associated with the same global source. If IT is constant, Kepler's third law follows directly, as does—for the circular projection—an acceleration proportional to ru207b². The observational identification IT ↔ GM then recovers the Newtonian limit. This result does not constitute a microscopic derivation of gravity. The conservation of IT remains a physical hypothesis requiring further substantiation. The aim is to show, in an explicit and falsifiable manner, where the geometric identity ends, where the PG hypothesis enters, and how the classical limit is recovered.
Category: Mathematical Physics
[54] ai.viXra.org:2608.0057 [pdf] replaced on 2026-08-20 16:36:15
Authors: Mustafa Karatüm
Comments: 21 Pages. u200bVersion 2: Substantial theoretical updates, comprehensive mathematical corrections, refined equations, and expanded analytical framework. Cross-reference: Zenodo DOI: https://doi.org/10.5281/zenodo.22009221
We present the Topological String-Gradient Theory (TSGT), a framework in which space-time is discrete at the Planck scale and gravity is the gradient of the spacing between discreteelements ("pixels"). Two kinematic postulates—a spatial pixel strain set by the Newtonianpotential and an equal temporal strain—reproduce the weak-field Schwarzschild metric, in-cluding the full light deflection ∆θ = 4GM/c2b; this reproduction is by construction. The dis-crete substrate is a random Poisson sprinkling of density L−4p , which preserves Lorentz invari-ance statistically and removes the preferred-frame problems of lattice formulations; lattice-derived predictions of earlier versions are retracted. If cosmic expansion creates new pixelsrather than stretching existing ones—the only option compatible with an invariant Lp—thenPoisson fluctuations in the pixel count fix the cosmological term to ρΛ ≃ 2.8 × 10−27 kg m−3,within a factor of two of the observed value; this argument is Sorkin’s heuristic, followinghere from TSGT’s own postulates. Written locally, the number—volume correspondence isthe unimodular constraint; enforcing it in an Einstein—Hilbert action yields the trace-freeEinstein equations, making TSGT provably equivalent to General Relativity at the classicallevel. The framework’s independent content lies in the integer character of the pixel countand in the fluctuating dark-energy term it implies (w̸ = −1). Unresolved problems, includingthe absence of a dynamical equation for the pixel density, are listed explicitly.
Category: Quantum Gravity and String Theory
[53] ai.viXra.org:2608.0056 [pdf] submitted on 2026-08-15 16:39:02
Authors: Karl Simon
Comments: 11 Pages.
AbstractThe Standard Model perfectly describes the system of elementary particles and their interactions, yet it fails to explain why there are precisely three generations of quarks and leptons, and why quarks possess fractional electrical charges. Furthermore, it does not address gravity’s fundamental mechanism in forming spacetime. This paper presents a novel structural model to shed light on these open questions. The model explores how a fundamental particle theory can be constructed from the simplest possible combination of a single chiral particle (b) and its antiparticle (q). Through geometric reflection, four elementary components emerge (b, p, d, q), whose purely topological shapes directly encode chirality and helicity. By introducing an invariant isospin (iI) and an invariant hypercharge (iY), electric charge (Q) is defined as an emergent property of specific substructures within states. The model demonstrates that simple combinatorial rules spontaneously generate structural quartets consisting of one lepton alongside three isomeric quark structures, whose statistical charges correspond exactly to the fractional charges of quarks. [1]Crucially, the model resolves the classic mass paradox and fine-tuning problem of preon theories—where massive binding energies must artificially cancel bare energies—by introducing an intrinsic, algebraic subtraction mechanism within the relationship between the W, Z, and the electron. Through the structural combinations W+Z-W, W+Z-Z, and the complete subtraction W+Z-W-Z -> e, the dynamic mass generation of the weak bosons and the very low mass of the electron are derived directly from state definitions without free parameters. Within this framework, both mass and electric charge emerge as phenomena strictly bound to irregular helicity configurations, identifying the seemingly vanished binding energy as the structural energy equivalent of the electric charge. This mechanism mirrors the immense energy scales conceptually postulated in Majorana-like mass terms for right-handed states without charge. [6] Tthe Higgs boson is naturally identified not as a separate elementary particle, but as the massive, scalar excitation state of the fundamental vacuum (bpdq) showing an inherent structural preference for aligned, "regular" helicities that governs the mass generation and electrical charge of particles.Finally, a potential connection to geometric gravitation theory is suggested, reminiscent of historical attempts to explain gravity as a structural residue between electric attraction and repulsion [4] Here pairs of photons of spin 2 interact via a double spinflip with neutrinos as the fundamental building blocks of all matter.
Category: High Energy Particle Physics
[52] ai.viXra.org:2608.0055 [pdf] submitted on 2026-08-15 23:52:43
Authors: Frank W. Brown
Comments: 4 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
I present a multi-scale empirical data appendix verifying the field equations of Curved Temporal Inertia Cosmology (CTIC). This 1-page report compiles two automated verification ledgers running natively within the open-source repository. First, a sequential 3-detector LIGO/Virgo matched-filter analysis of event GW170817 targets the model's non-axial metric twisting shear envelope (h_omega) using a stable time-domain RMS normalization layer. The network trace reveals an unmistakable, high-confidence Signal-to-Noise Ratio (SNR) peak of 28.2123 at LIGO Hanford (H1), an expected sub-threshold validation of 7.3335 SNR at LIGO Livingston (L1), and a baseline antenna blind-spot trace of 5.4227 SNR at Advanced Virgo (V1). Second, the report maps a macroscopic coordinate domain ledger tracking a triaxial ellipsoidal subcluster grid across 40 morphologically diverse galaxy clusters, yielding a uniform observational deviation margin of < 2.0% using strictly 100% visible baryonic mass parameters. Complete automated replication pipelines are open-sourced at: https://github.com/LiamLumen/CTIC-Quantum-Dynamics
Category: Relativity and Cosmology
[51] ai.viXra.org:2608.0054 [pdf] submitted on 2026-08-14 20:08:25
Authors: Arunas Ostasevicius
Comments: 5 Pages.
The paper presents a fundamental historical and mathematical exposure of the kinematic foundations of the Special Theory of Relativity (SR). Based on a rigorous analysis of the original text of J. C. Maxwell’s Treatise on Electricity and Magnetism (1873, paragraphs 600—601), it is proved that the original equations of the electromagnetic field initially contained total (material) time derivatives and convective field drift operators (v · ∇). It is demonstrated that Maxwell’s original system was naturally invariant under classical Galilean transformations in absolute Euclidean space. The study establishes that SR arose as an artificial geometric artifact (Lorentz transformations, Minkowski metric) designed to compensate for the fatal castration of the field equations by O. Heaviside, who forced the convective velocity of the coordinate axes to zero and replaced the total derivative with a partial one. The physical reality of Maxwell’s convective drift is confirmed by the one-way mirrorless experiments of S. Marinov and R. De Witte, completely rendering the metric space-time paradoxes of modern physics unnecessary.James Clerk Maxwell, Oliver Heaviside, Galileo invariance, total derivative, convective term, Stefan Marinov, Roland De Witte, Special Relativity critique.
Category: Relativity and Cosmology
[50] ai.viXra.org:2608.0053 [pdf] submitted on 2026-08-14 13:31:35
Authors: Joseph Shaffer
Comments: 6 Pages.
Spacetime, matter, and physical law emerge as macroscopic unitary outcomes of a system converting high-energy chaos into optimal stability. The universe begins as a chaotic tension matrix (Domain A) filled with unstable local maxima. A tension-bearing phase boundary-the mat-absorbs chaotic shear vectors, flattens them into coherent spatial gradients, and locks unfilterable stress peaks into localized matter structures. When the system crosses a critical radius threshold, a subcritical pitchfork bifurcation rigidifies the mat and produces the calm fabric (Domain B). Stability arises from the large-number postulate: chaotic modes interacting in enormous numbers become unresolvable, leaving only stable structures visible. Spacetime and matter are the macroscopic shadows cast by submerged chaos.
Category: Astrophysics
[49] ai.viXra.org:2608.0052 [pdf] submitted on 2026-08-13 12:06:32
Authors: XinXin Li
Comments: 5 pages. CC BY 4.0.
We establish an exact algebraic identity connecting the cumulative near-conjugacyerror Eσ of a base-6 circle-rotation model of the Collatz map (HonarvarShakibaei Asli, 2026) with the terminal correction ε in the classical stopping-timeidentity. For a convergent Syracuse orbit, Eσ = 1 − log6(5n0+1)+ (log2 n0 + ε)·log6 2, in which the Syracuse stopping time τcancels exactly via the change-of-base formula log2 6 · log6 2 = 1.Consequently Eσ = O(1) ⇔ ε = O(1) ⇔ Σ 1/ni−1 = O(1), so theboundedness of the reciprocal sum becomes the central open question. The identity isverified to machine precision (≤ 2×10−15) for every tested n0 ≤ 77031.
Category: Number Theory
[48] ai.viXra.org:2608.0051 [pdf] submitted on 2026-08-12 20:12:06
Authors: Arunas Ostasevicius
Comments: 6 Pages. 2 figures.
An alternative concept for describing the dynamics of celestial bodies based on non-linear self-oscillations in a material cosmic medium is presented. From first principles — Boltzmann's kinetic equation — a closed system of two coupled quaternionic equations is rigorously derived. These equations describe the orbital motion of a planet's center of mass and its axial rotation as stable phase attractors (limit cycles). Using the analytical method of phase averaging, the deformation of Mercury's phase trajectory under the influence of polytropic changes in the parameters of the medium near the Sun is calculated. The superiority of non-linear oscillation theory methods over the geometrization of spacetime is demonstrated, allowing for the complete abandonment of the cumbersome linear algebra apparatus of General Relativity and the postulation of mystical initial conditions.planetary dynamics, self-oscillations, Boltzmann kinetic equation, quaternion, limit cycle, phase averaging, cosmic medium, Ether, perihelion precession, general relativity alternative
Category: Astrophysics
[47] ai.viXra.org:2608.0050 [pdf] submitted on 2026-08-12 20:10:56
Authors: Khazri Bouzidi Fethi
Comments: 9 Pages.
We study the Diophantine equation 1/p_1 = 1/p_2 + 1/p_3 + 1/p_4 for distinct primes p_1, p_2, p_3, p_4, a special case of the Sierpiński—Schinzel unit-fraction equations. We introduce a spectral coherence threshold R, derived from an exact infimum formula for a normalized exponential sum over the primes involved via the Kronecker—Weyl equidistribution theorem, and show that R = 1/2 is its sharp transition value. For three primes, we establish an exact identity linking R to prime gaps, giving a new proof that no three consecutive primes satisfy the analogous three-term equation. For four primes, we combine this classification with an exact divisor-based algorithm to search over 6 times 10^8 configurations, finding no solution for p_1 le 5431 but reporting the closest known near-solution. We prove that no solution can occur with the three larger denominators in arithmetic progression, and record a short, fully general divisibility argument showing that no such equation admits a solution in distinct primes for any number of terms — clarifying explicitly that this fact concerns single-prime denominators only, not the composite-denominator setting central to the Sierpiński—Schinzel conjectures.
Category: Number Theory
[46] ai.viXra.org:2608.0049 [pdf] submitted on 2026-08-11 12:20:40
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure. Exact d=5 inverse commutator cost: 12 Horn chambers, optimal-rank law, sharp tax [1,5/2], triangular synthesis, and reproducible rational certificates.
For a prescribed traceless Hermitian five-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. If g_i=lambda_i-lambda_{i+1} are the ordered spectral gaps, the answer is the maximum of six explicit rational linear forms and their reversals. Exact Littlewood-Richardson enumeration gives 142 Horn inequalities. Twelve sparse dual identities prove the lower facets, and twelve rational singular-spectrum maps attain them; exact cone certificates prove completeness without sampling. In contrast with the two qutrit facets and four four-level facets, dimension five has twelve exposed facets and open chambers that force rank four. For every nonzero target, the least rank of an optimal factor is max(n_+(F),n_-(F)). We also prove the sharp tax 1 <= kappa_5/(||F||_1/2) <= 5/2 with complete equality loci, and the exact balanced triangular perimeter S_2^2=12 sqrt(3) kappa_5. Two rational certificates and an independent deterministic LP campaign accompany the paper.
Category: Mathematical Physics
[45] ai.viXra.org:2608.0048 [pdf] submitted on 2026-08-11 13:00:56
Authors: Lluis Eriksson
Comments: 10 Pages.
Under an explicit noncontextual homogeneous-response ansatz for rank-one quantum effects, we study normalization on every unitary rotation of a fixed finite POVM. The orbit-normalization operator diagonalizes on the projective harmonics of complex projective space. We derive its weighted all-degree singular spectrum and show that the smallest non-Born spectral value is the sharp condition number controlling distance from the affine space of trace-one Hermitian quadratic responses. For dimensions at least three, the high-degree spectrum of a finite seed converges to the sum of squared aggregate ray weights; for an outcome-simple equal-trace seed with N outcomes, the limit is d squared divided by N. Combining this ceiling with the forced geometry of the two smallest tight frames solves the global equal-trace design problem in every dimension d at least five. An orthonormal-basis seed uniquely maximizes the all-degree Born-rigidity gap, with value d minus 6 divided by d plus 1, up to unitary equivalence and outcome relabeling. Every distinct-outcome overcomplete seed in the stated class is strictly worse. By contrast, every weighted complex projective 2-design has a degree-two nullspace and therefore zero rigidity gap. Thus measurements optimal for state tomography can be maximally non-rigid for this covariant normalization objective. The result concerns one-step response fields and does not derive state update, intrinsic randomness, or microscopic particle dynamics.
Category: Mathematical Physics
[44] ai.viXra.org:2608.0047 [pdf] submitted on 2026-08-11 13:47:42
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Reproducible certificate and independent verifier are linked in the PDF.
A passive lossless network may route the same k-dimensional input channel to different output subspaces at different frequencies. Every two-frequency restriction can be cheap while the joint task is not. For L distinct boundary frequencies and mutually orthogonal prescribed output k-planes, we prove that the minimum McMillan degree among square finite rational-inner transfer matrices regular at the interpolation nodes is exactly k(L-1). Each pair alone requires degree k, so the largest two-node minimum underestimates the global memory by the unbounded factor L-1. The result is independent of node spacing. Necessity follows both from a zero budget for an analytic minor and from a Pick-Stein displacement identity whose negative inertia cannot exceed realization rank. Sufficiency follows from an explicit positive Pick completion. Beyond exact orthogonality, we derive a general cross-frequency inertia certificate, a gauge-independent span bound, an open robust region preserving the integer memory count, and a fail-closed noisy-eigenvalue certificate. Deterministic code tests arbitrary nodes, synthesizes minimal conservative realizations, and independently verifies the stated identities.
Category: Mathematical Physics
[43] ai.viXra.org:2608.0046 [pdf] submitted on 2026-08-11 15:21:20
Authors: Lluis Eriksson
Comments: 11 pages, 2 tables, 1 figure. Exact spin-j echo spectra, finite frames with stability bounds, sharp link-OS/sinc boundary, and connected HS nuclear cutoff.
Four balanced spin kicks along the vertices of a regular tetrahedron generatean order-dependent eight-pulse echo. We prove that all 24 echo orders have oneconjugacy class in SU(2). Haar randomization of only the global orientationtherefore gives an order-law-independent, self-adjoint random-unitary channelon every spin-j matrix algebra. Its exact eigenvalues are normalized SU(2)characters, lambda_l=U_{2l}(q)/(2l+1), with multiplicity 2l+1 and an explicitfinite-pulse architecture polynomial q=1-A/2. The maximal link-reflection-positive interval connected to zero is alpha<=pi/(4j+1), with an exact endpointequation and a finite OS Hamiltonian under strict inequality. In the doublescaling N=4j+1, y=xi/sqrt(N), the full tower converges uniformly tosinc(8xi^2u). This gives the sharp full-tower boundary xi_c=sqrt(pi/8), acritical boundary law N lambda_top -> 3pi/8-2s, an explicit scaled mass profile,and an ultraviolet heat-trace integral. The fixed-rank limit recovers the fuzzy-sphere Laplacian. Poissonization yields a genuine CPTP semigroup and an exactmany-body connected nuclear profile exp(3e^-c)-1. Symbolic and deterministicmatrix certificates accompany the manuscript.The Haar average also has explicit exact finite implementations. A classicalpositive Gauss--Legendre/trapezoidal cubature at bandlimit 4j needs(4j+1)(2j+1) order-conditioned frames, or (4j+1)^2(2j+1) frames when the sameframe list must be order oblivious.The common-class proof reduces the 24 orders to the even and odd A4 orbits.For finite implementations, a separate stability bound controls l1 weighterror, orientation displacement, and pulse perturbations; total variationagainst Haar is not used for discrete frames.
Category: Quantum Physics
[42] ai.viXra.org:2608.0045 [pdf] submitted on 2026-08-11 15:57:16
Authors: Lluis Eriksson
Comments: 9 pages, 1 figure, 1 table. Exact generic memory law, colliding-target discontinuity, noisy projector certificate, and three-line phase diagram.
At L boundary frequencies, a passive lossless network must route one fixed k-dimensional input channel to prescribed output k-planes. For targets with joint span dimension r, every square finite rational-inner interpolant satisfies the sharp universal sandwich r-k <= d_min <= k(L-1). Direct-sum targets therefore have exact minimum McMillan degree k(L-1); when N >= Lk this maximal-memory locus is open and dense. The paper gives an explicit positive Pick completion, a realization- and inertia-based lower bound, a family of targets that collide while retaining maximal exact degree for every nonzero opening, an exact quadratic certification margin, and a fail-closed noisy projector test. For three scalar target lines it also proves the complete phase diagram: degree zero for one common line, degree one exactly for three distinct coplanar lines, and degree two otherwise. Deterministic certificates and an independent implementation accompany the proofs.
Category: Mathematical Physics
[41] ai.viXra.org:2608.0044 [pdf] submitted on 2026-08-11 19:17:05
Authors: Keiji Yoshimura
Comments: 22 pages. English translation edition v1.0.1-EN1 of the Japanese scientific baseline v1.0.1. Associated public reproducibility repository is linked in the manuscript.
This study reconstructs the Japanese rice industry not as a single price chain but as a multi-actor network in which goods, money, information, risk, authority, and explanations move at different speeds and levels of aggregation.Using public statistics, administrative and legal records, industry statements, and a purposively sampled media corpus, the audit fixed price stage, unit, period, product, and contract conditions before testing end-to-end traceability.Public sources provide substantial visibility into quantities, stage-level averages, production costs, inventory volumes, retail transaction prices, and policy outputs. They do not, however, permit continuous monetary tracing of the same contract, inventory cohort, or product.Four principal breaks were identified: the producer's final receipt, inventory acquisition cost, absolute wholesale selling prices, and product-level retail procurement, costs, and profits. Consequently, price-stage differences or bridge residuals cannot by themselves identify wholesale or retail profit, profiteering, or the contribution of a single actor.Policy responses since 2025 shifted from conditional auctions to downstream direct contracts, official self-review, and statistical and legal redesign, while the pure retail-price effect of reserve-rice releases and the practical effectiveness of the new reporting system remain unidentified.A staged transparency architecture is proposed as a design implication: common metadata and measurement crosswalks, anonymous price-bridge pilots, and eventually an integrated six-flow and cohort infrastructure.The study does not determine a fair price, a profiteering actor, collusion, or a pure policy effect; it specifies what is observable, where public traceability breaks, and what evidence would update the conclusions.
Category: Economics and Finance
[40] ai.viXra.org:2608.0043 [pdf] submitted on 2026-08-12 01:48:33
Authors: Joseph Mcgreevy
Comments: 20 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We formalize a unified geometric and representation-theoretic architecture bridging the continuous deformation of modular parameter spaces to the discrete, quantized structures of arithmetic number fields and local gauge theories. In the first part of this work, we present astructured verification of the Birch and Swinnerton-Dyer (BSD) Conjecture for Rank 2. By defining a stationary modular wave equation via the Maass-Laplacian, we isolate the weight-12 cusp form ∆ as an on-shell, massless zero-mode. At the bad reduction prime p = 691, this continuous flux degenerates against a singular cusp, collapsing the higher-dimensional geometric cycles of the 3-dimensional Kuga—Sato variety W2 onto the n = 0 neutral core of the Schmid weight filtration light cone. We construct the explicit 2×2 p-adic Syntomic Comparison Matrix, proving that its determinant is non-zero and non-degenerate under local-to-global stress at the fracture wall if and only if the p-adic N´eron—Tate height regulator is non-singular. In the second part, we document a precise homological parallel between this arithmetic localization and the structural stability constraints of quantum gauge fields. We demonstrate that the mechanism passing the E2 quasi-modular anomaly through higher-weight Eisenstein series mirrors the scaling of a gauge connection protecting a positive-definite kinetic energy landscape. This continuous propagation forces a compact Lie group topology, which shatters at the 691 boundary into an 11-dimensional coefficient space—casting a direct arithmetic shadow onto the χ 11 odd eigenspace of the cyclotomic minus class group via the Herbrand—Ribet theorem. We present this unified framework not as a physical identity, but as a rigid representation-theoretic blueprint governing Rank-2 root system degenerations at the boundary of a continuum.
Category: Mathematical Physics
[39] ai.viXra.org:2608.0042 [pdf] submitted on 2026-08-10 08:28:18
Authors: Lluis Eriksson
Comments: 17 pages, 4 figures, 2 tables. Includes robust separation theorems, a vacuum-complete Ramsey model, 60-digit certificates, open-source code, frozen ledgers, and passing CI checks.
We study whether passive reservoir filtering can suppress decoherence more effectively when its channel mixing is irreducible, even after fixing the passband responses and rational complexity. For every integer S ≥ 5, we construct an explicit causal inner six-port network with three signal and three vacuum-loss ports. Its signal block is a rational Schur transfer satisfying 3(S−1) delayed full-spark tangential calibrations and exhibiting exponentially small leakage on two stop arcs. In contrast, every transfer of the same bidegree possessing a constant nontrivial reducing channel and satisfying the same calibrations retains unit stopband norm.We strengthen this exact separation with a quantitative finite-error obstruction: for calibration defect δ and sampled reducing-line defect β, comparator leakage is bounded below by [1−C_S(δ+β)]_+, with C_S given explicitly by finite singular-value margins. A scalar Schur construction proves that every bound of this form must deteriorate at least as 2 exp(9S/20)(1+o(1)); hence uniform robustness is impossible for the chosen clustered calibrations.For uniformly nondegenerate bath spectra, the signal-level separation is squared at the Kossakowski-rate level. A closed Markov pure-dephasing model includes all auxiliary vacuum ports exactly, producing an architecture-independent measurable baseline and an explicit total Ramsey-rate advantage. Finally, we prove that strong passive suppression requires large dwell time: under a peak-delay budget D, the rate-improvement factor is asymptotically at most quadratic in D/S. The construction therefore moves the coherence-maintenance resource into passive memory, vacuum noise and conditioning rather than eliminating it. All certificates, figures and numerical audits are publicly reproducible.
Category: Quantum Physics
[38] ai.viXra.org:2608.0041 [pdf] submitted on 2026-08-10 10:22:35
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Analytic proofs and reproducible certificates; code, numerical audits and release checks are available in the linked GitHub repository.
How many internal passive modes are required to transmit prescribed quantum noise channels without loss while suppressing all signal directions elsewhere? We prove an architecture-independent answer for finite-dimensional rational networks. Let a causal rational inner scattering matrix S have McMillan degree n, signal block G, and complementary loss block C. At distinct regular boundary frequencies, suppose that G is isometric on input subspaces of dimensions k_j. If G is a strict contraction at one other frequency, then sum_j k_j ≤ n.Every lossless direction lies in the kernel of C; a nonzero maximal minor of C therefore has a zero of multiplicity at least k_j. Exterior powers of a minimal Blaschke—Potapov factorization show that no minor can have more than n zeros. The same factorization yields the exact topological delay identity(1/2π) ∫ tr Q(θ) dθ = deg_McM S = n,where Q = −i S* ∂θS is positive semidefinite. Thus lossless calibration multiplicity is bounded by integrated Wigner—Smith delay. The bound is sharp in every dimension. We establish robustness under analytic passive perturbations, prove why unstructured approximate samples cannot imply a degree bound, and show that a previously constructed six-port reservoir filter is universally optimal up to six internal states. Proofs and numerical certificates are reproduced by the linked public repository.
Category: Quantum Physics
[37] ai.viXra.org:2608.0040 [pdf] submitted on 2026-08-10 11:14:40
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible certificate, source and verifier: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.3-robust-spectral-routing
Exact interpolation can force the internal degree of a passive network, but laboratory calibrations are approximate. We prove a sharp frequency-domain speed limit requiring neither exact zeros nor analytic continuation away from the measured frequency axis. Let (S(e^{itheta})) be an absolutely continuous unitary scattering path with positive Wigner—Smith generator (Q(theta)=-iS(e^{itheta})^astpartial_theta S(e^{itheta})succeq0). If a fixed (k)-dimensional input subspace is routed approximately between complementary output sectors with amplitude leakages (varepsilon_p,varepsilon_s), define (alpha=[pi/2-arcsinvarepsilon_p-arcsinvarepsilon_s]_+). Every transition then requires Wigner—Smith trace action at least (2kalpha) and largest-proper-delay action at least (2alpha). Costs add over disjoint frequency arcs. For a rational inner network of McMillan degree (n), (M) alternating pass/stop pairs imply (nge 2Mkalpha/pi), recovering (nge Mk) at zero error. An explicit (2k)-port interferometric family attains the bounds for every admissible error pair. A tomography-error corollary converts finite scattering measurements directly into certified degree and delay lower bounds. Reproducible certificates audit equality cases, positive-block inequalities and random Blaschke—Potapov products.
Category: Quantum Physics
[36] ai.viXra.org:2608.0039 [pdf] submitted on 2026-08-10 12:58:55
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact symmetric-gauge and Ky Fan speed limits for passive networks, with sharp constructions, robustness bounds and open code.
A subspace quantum speed limit usually records only the largest canonical angle. Passive scattering theory usually records either the largest proper delay or their total trace. Both compressions discard how a rank-k routing event is distributed across modes. We derive the missing vector law: the integrated spectral-spread vector weakly majorizes twice the canonical-angle vector. More strongly, for every symmetric gauge Φ and every pair of k-subspaces in N ≥ 2k dimensions, we solve the variational problem exactly: the minimum spectral-spread action is 2Φ(β). The same value holds for the leading-proper-delay action under positive generators, and one constant coupled-mode path minimizes all gauges simultaneously. The Ky Fan members recover the bandwidth limit, strengthen the trace-action law, and expose every intermediate modal budget. An exact nonnegative slack decomposition separates common-mode delay, inefficient spectral coupling, and nongeodesic subspace motion. Robust corollaries convert heterogeneous pass/stop leakage spectra and finite tomography errors into certified Lorenz curves for delay and, for rational inner networks, McMillan-degree lower bounds. A deterministic artifact tests 8,192 random generators, 1,536 time-dependent paths, sharp equality families, and 2,048 noisy tomography instances.
Category: Quantum Physics
[35] ai.viXra.org:2608.0038 [pdf] submitted on 2026-08-10 14:22:14
Authors: Lluis Eriksson
Comments: 13 pages, 2 figures. Adds exact quintic obstruction P_H, sharp Theta(n^-3/2), an O(n^-2) fourth level, and an exact attaining example. AI assistance disclosed.
Repeated projective measurements are usually discussed either in the ballistic Zeno scaling or after reduction to classical outcome probabilities. We study a different regime in which each nonselective measurement retains a full matrix algebra inside every degenerate outcome block. Let E(X)=sum_a P_a X P_a, let E_tau be its rotation by exp(-i tau H), and close one cycle by Phi_tau=E E_tau E. We prove, uniformly on compact time intervals and in diamond norm, that Phi_{sqrt(t/n)}^n converges to exp(-tK)E, where K=E ad_H(1-E)ad_H E=C_H^* C_H. The limit is a genuinely quantum Markov semigroup on the direct sum of the block matrix algebras, with explicit jumps sqrt(2) P_b H P_a. Beyond upper bounds, we identify three exact local obstructions for the unprocessed physical product. The cubic map M_H produces a nonzero n^{-1/2} coefficient; after it vanishes, the quartic product obstruction J_H produces a nonzero n^{-1} coefficient; after both vanish, the quintic obstruction P_H produces a nonzero n^{-3/2} coefficient. If all three vanish, the error is O(n^{-2}). All three coefficient transforms are injective. An exact three-record algebraic example has M_H=J_H=0 but P_H nonzero, proving that the third branch is attained. The fixed algebra is A intersect {H_off}', and the least singular value of the commutator frame C_H defines a noncommutative connectivity gap. In the primitive case that gap is the exact exponential mixing exponent in diamond norm and is Lipschitz robust under Hamiltonian perturbations. Rank-one blocks reduce exactly to twice the squared-coupling graph Laplacian. An eight-dimensional rational architecture with four qubit blocks is certified irreducible; its gap is the unique root in (0.4545,0.4547) of an explicit quartic. Symbolic certificates, semidefinite diamond-norm replays, and convergence tests accompany the paper.
Category: Quantum Physics
[34] ai.viXra.org:2608.0037 [pdf] submitted on 2026-08-10 15:20:28
Authors: Lluis Eriksson
Comments: 10 pages, 1 figure. Exact diamond curvature, a discrete Stokes law, balanced semigroup integration, and a sharp qubit action bound. AI use disclosed.
The order of short operations is normally a microscopic detail. We show that a fixed degenerate measurement turns it into an operational curvature with an exact macroscopic readout. Let E retain a block matrix algebra, and let two words apply the same short Hamiltonian kicks in different orders, with the same nonselective pinching after every kick. Their leading difference is `-i tau^2 ad(F) E`, where F is the sum of `i[h_j,h_k]` over pairwise inversions. This gives a discrete non-Abelian Stokes law. Its diamond-norm coefficient is exactly the largest spectral diameter of a block of F, and therefore fixes the leading optimal channel-discrimination advantage. Under first-order balance, all permutations have the same dissipator while their geometric Hamiltonians differ exactly by F, so local curvature integrates into distinct diffusive quantum Markov semigroups. We characterize contextual invisibility, the rank-one classical boundary, and inverse-success amplification under postselection. Every retained Hamiltonian modulo the block center is realizable by a balanced three-kick loop. For a qubit block we prove the sharp action law `kappa <= S^2/[m tan(pi/m)]`, attained by regular planar kick polygons. An integer-Pauli four-kick architecture saturates the bound and supports primitive dissipation. Symbolic, semidefinite, and convergence certificates accompany the paper.
Category: Quantum Physics
[33] ai.viXra.org:2608.0036 [pdf] submitted on 2026-08-10 15:47:43
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Reproducible code and certificates: https://github.com/lluiseriksson/finite-sample-spectral-certificates/releases/tag/v1.7-complete-continuous-delay-regions
Lower bounds do not determine which resource profiles are physically attainable. We close the continuous inverse problem for passive subspace transport. Let two rank-k subspaces in C^N, N >= 2k, have ordered canonical angles beta, and let q_j be the integrated leading eigenvalues of a positive generator Q = -iS* dS/dt. We prove the exact equivalence: q is attainable if and only if 2 beta is weakly majorized by q. Every feasible profile has a compiler using at most k+1 mutually commuting positive generators of rank at most k, with constant ordered top spectrum. Analytic rationality adds an integer-valued resource: for two boundary frequencies, the least McMillan degree of an inner matrix sending a fixed input subspace to two prescribed output subspaces equals the number of nonzero canonical angles. We also give a fail-closed finite-error certificate for both resources from noisy projectors.At multiple frequencies, Wigner-Smith delay is only the block diagonal of a boundary de Branges-Rovnyak Pick matrix. This positive matrix is the Gram matrix of frequency-excited internal states and has rank bounded by the McMillan degree. Its spectrum yields robust degree certificates and unavoidable model-reduction tails. An exact example exhibits identical local proper delays for degree-one and degree-two devices while their Pick ranks distinguish them. Deterministic code reconstructs the compilers, tests 2,240 randomized theorem interfaces, checks the strict separation, and independently replays the certificate.
Category: Quantum Physics
[32] ai.viXra.org:2608.0035 [pdf] submitted on 2026-08-10 16:16:46
Authors: Lluis Eriksson
Comments: 12 pages, 1 figure. Sharp qudit action laws, exact 1/12 covariance, O(n^-1) GKLS diffusion and a sqrt(n) clock barrier.
A balanced ordered loop of retained Hamiltonians generates a second-order geometric Hamiltonian. We solve its higher-rank action problem and determine what remains when the order record is erased. For every matrix dimension and every number of kicks `m >= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper.
Category: Quantum Physics
[31] ai.viXra.org:2608.0034 [pdf] submitted on 2026-08-10 19:10:19
Authors: Lluis Eriksson
Comments: 13 pages, 1 figure. Exact qutrit cost, tetrahedral gap and twirl, physical-word limit, quantified beta trichotomy and initial layer.
A balanced sequence of short Hamiltonian kicks has zero first-order drift but retains an order-dependent commutator holonomy. For a traceless qutrit target with ordered eigenvalues, we solve the inverse Hermitian-commutator problem exactly: its minimum product Hilbert-Schmidt norm is the larger adjacent spectral gap, equivalently half the trace norm plus the absolute middle eigenvalue. This yields the exact minimum action of a balanced three-kick realization and identifies a middle-eigenvalue cost tax between 1 and 3/2. Among four equal-norm balanced qubit kicks, the forgotten-order curvature gap is at most `S^4/108`, with equality only for a regular tetrahedron. Its 24 orders generate exactly the six Pauli holonomies, so the finite twirl is depolarizing and an explicit inverse-cosine schedule realizes any depolarizing semigroup exactly at every finite step count. We then derive the diffusion limit from complete echoed, pinched physical words, obtaining an explicit `O(n^-1/2)` diamond-norm bound. Off-block pulses of size `y^(1+beta)` produce a sharp trichotomy: irrelevant for `beta>1`, additive at `beta=1`, and Zeno-projective for `0<beta<1`; a quantitative compression bound gives uniform convergence away from zero and an explicit initial-layer profile. The complete implementation has serial action proportional to `n^(3/4)`. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[30] ai.viXra.org:2608.0033 [pdf] submitted on 2026-08-10 19:28:35
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. Exact action-memory theorem with explicit compiler and independent verification. Code: github.com/lluiseriksson/finite-sample-spectral-certificates
A passive lossless network pays two different costs when it rotates a signal subspace over a frequency arc: a continuous Wigner—Smith action and an integer McMillan memory. Known Grassmannian length bounds and rational-inner degree identities constrain these resources separately. For the stated finite rational-inner class, we determine their joint attainable region exactly. Let two rank-k subspaces have principal angles βj, put B = Σj βj and let r be the number of nonzero angles. For a square finite rational inner transfer matrix of degree at most d, define the arc action A = ∫I tr Q(θ)dθ, where Q = −iS*∂θS is positive semidefinite. If B > 0, the exact feasible set is d ≥ r and 2B ≤ A ≤ 2πd − 2B. Both faces are attained. Equivalently, dmin(A) = max{r, ⌈(A + 2B)/(2π)⌉}. The upper face is a return cost: the complementary arc must rotate the subspace back, while the full-circle trace action is exactly 2π times the degree. We prove sufficiency by an explicit compiler of normalized rank-one Blaschke—Potapov gates; it realizes every interior point and both faces, including rank-deficient and orthogonal cases. When the endpoint subspaces coincide, the region changes discontinuously to A ∈ [0, 2πd), with the upper endpoint open. We derive fail-closed noisy degree certificates and give a multi-frequency warning using classical boundary Nevanlinna—Pick theory: three pairwise degree-one routing tasks can require degree two jointly. For orthogonal-line data the obstruction is a frame-independent cycle phase, exhibited by an exact positive semidefinite Pick completion with spectrum (2,1,0). Deterministic code compiles random points of the diamond, constructs the degree-two colligation, and is replayed by an independent verifier.
Category: Mathematical Physics
[29] ai.viXra.org:2608.0032 [pdf] submitted on 2026-08-10 20:30:59
Authors: Lluis Eriksson
Comments: 11 pages, 1 figure. New paper: positive physical transfer from forgotten order, exact tetrahedral spectrum, Hausdorff gap certificates, and Gaussian level control.
A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript.
Category: Quantum Physics
[28] ai.viXra.org:2608.0031 [pdf] submitted on 2026-08-10 21:34:32
Authors: Lluis Eriksson
Comments: 9 pages, 2 figures. Exact d=4 inverse commutator cost from four Horn facets, all-strata optimal-rank law, sharp tax [1,2], loop action, and reproducible certificates.
For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript.
Category: Quantum Physics
[27] ai.viXra.org:2608.0030 [pdf] submitted on 2026-08-10 03:07:25
Authors: Alistair B. Carter
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper presents a foundational, pre-geometric hydrodynamic framework that models spacetime geometry, gravity, and quantum phenomena as emergent thermodynamic properties of an 8-dimensional non-associative fluid vacuum. Parameterized by complexified octonions (the bioctonions), the state space transitions from linear Hilbert spaces to the power-associative matrix algebra of the 27-dimensional Exceptional Jordan Algebra (J3(O)), bound by an F4 automorphism envelope.The framework bridges two historically disparate domains: division-algebraic particle physics (Dixon, Günaydin, Gürsey, Furey) and analogue gravity in condensed matter vacuum models (Unruh, Volovik, Visser). By synthesizing Volovik's superfluid vacuum paradigm with bioctonion algebraic models of Standard Model gauge symmetries, we demonstrate that forces and matter arise natively as topological deformations of a single continuous medium.We clarify that while complexified octonions form a non-division, power-associative algebra with zero divisors, these properties are fundamental assets to the physics. Anti-commutativity natively encodes Fermi-Dirac statistics and the Pauli exclusion principle; non-associativity generates gauge field curvature, non-linear fluid friction, and temporal processing latency; and zero divisors yield idempotent projection operators that isolate chiral spin states and light-like null trajectories without external metric constraints.We resolve four central mathematical and physical hurdles in non-associative field theories: (1) Macroscopic Matrix Insulation: We prove via real-projection identities and Jordan trace associativity Tr([X, Y, Z]ˆ) = 0 that diagonal observables remain strictly real and associative, insulating observers from off-diagonal phase perturbations. (2) Free Particle Proper Time: We formalize proper time (dτ) as a deformed disformal metric invariant containing an associator correction term, enabling free particle weak decay while preserving temporal latency in high-shear regimes. (3) Rigorous Non-Associative Calculus: Using directional differential operators, we prove free wave propagation in the 8D vacuum is strictly anomaly-free due to octonionic alternativity. (4) Multi-Particle Containment: We construct an explicit 56-dimensional E7 Freudenthal module mapping that proves widely separated particles decouple into independent quartic invariants, preventing non-local parenthetical phase contamination.Finally, the bulk modulus of the fluid matrix resolves the vacuum catastrophe, and theoretical falsifiability is established via a parameter-free derivation of non-conservative orbital energy shifts driven by vacuum vorticity (Ωvac), deterministically matching empirical planetary flyby anomalies.
Category: Quantum Gravity and String Theory
[26] ai.viXra.org:2608.0029 [pdf] submitted on 2026-08-10 02:01:56
Authors: Lluis Eriksson
Comments: 18 pages; Exact-arithmetic, numerical, and Lean/mathlib reproducibility artifacts are linked in the paper.
Scalar Chebyshev filtering treats every vector in a block Krylov iterate with the same polynomial, while simultaneously diagonalizable matrix coefficients amount to independent scalar filters after a fixed channel rotation. We study the larger class of Hermitian matrix-polynomial filters under tangential pass constraints. Already at fixed channel dimension d=3, we construct rationally generated signatures with quantitative full-spark margin for which an irreducible symmetric filter has stopband leakage O(exp(-cN)). In contrast, every exactly calibrated symmetric coefficient family with any common nontrivial invariant channel subspace has leakage at least one; this comparator strictly contains the pairwise-commuting class and permits a fully noncommutative 2 by 2 block. A quantitative theorem covers approximately reducible filters by charging their sampled off-block coupling together with calibration error. The signature margin and the admissible combined error are both exp(-O(N)), not exp(-N^3). This exponential scale is unavoidable: for arbitrary pass nodes and signatures in the same separated bands, an explicit scalar binomial-tail polynomial has both pass error and stopband leakage at most exp(-2N/81). Thus constant-error separation is impossible, while the irreducible construction achieves the correct exponential scale class. An affine cosine substitution gives the same robust law for fixed-latency reciprocal linear-phase MIMO FIR filters. We also give an exact rational five-tap certificate with stopband norm at most 25/32 and prove that its advantage survives reducible calibration errors delta < 7/1920. A second exact-arithmetic certificate is calibrated from a public triaxial pump-vibration data set: it gives leakage below 0.96 versus one for every exactly calibrated reducible symmetric class, while its maximum directional error on six held-out records is 0.00385. In a frequency-domain-decomposition test on the frozen held-out cospectra, filtering rotates the leading modal direction by at most 0.222 degrees and changes its leading spectral ordinate by at most 2.4 × 10^-5 relatively. Numerical programs test the mechanism and expose an ordinary graph-denoising setting in which scalar Chebyshev filtering is instead preferable. Tangential matrix interpolation, MIMO filtering, scalar two-band approximation and convex FIR design are not claimed as new; the contribution is the fixed-order reducible/irreducible separation together with its two-sided calibration scale.
Category: Digital Signal Processing
[25] ai.viXra.org:2608.0028 [pdf] submitted on 2026-08-09 19:02:29
Authors: Arunas Ostasevicius
Comments: 8 Pages. 2 Figures
This paper expands the quaternionic field framework into the fully dynamic regime of electrodynamic radiation, autowave propagation, and resonance absorption by treating the physical vacuum as a deterministic, compressible elastic medium of sub-planckian vacuum bubbles (the Wheeler substrate). By deploying a non-linear second-order Verhulst—Van der Pol logistic regulator, we establish a rigorous four-fold taxonomy of substrate kinematics: laminar drift, collective macro-convection, pulse shocks, and high-frequency volumetric oscillations. We deconstruct the classical Maxwellian displacement current, mapping it as the literal velocity of elastic shape deformation within the bound bubble matrix under finite field viscosity. This hydrodynamic ontology eliminates the historical energy-divergence paradoxes and provides a transparent mechanical contrast between the closed, dissipative conduction currents of conventional technology and the open, non-local resonant autowave transfers observed in Tesla-Meyl single-wire topologies. Finally, the intra-atomic current of the hydrogen atom is reinterpreted as a closed, non-radiating toroidal self-circulation of the substrate under a 2:1 gyroscopic resonance condition. We define quantum transitions not as stochastic jumps, but as a causal two-stage process consisting of external acoustic pumping (vortex energy accumulation) followed by a non-linear quadratic boundary disruption that releases an isolated, indivisible longitudinal-transverse quaternionic electromagnetic wave packet with a strict pi/2 phase quadrature between the scalar potential S and the transverse vectors.8
Category: Quantum Physics
[24] ai.viXra.org:2608.0026 [pdf] submitted on 2026-08-09 18:42:43
Authors: Bing Zhang, Aizhong Jia
Comments: 29 Pages.
The Graviton Condensation Cosmology (GCC) framework posits that macroscopic gravity emerges from the condensation of spin-2 collective quadrupole excitations (GQR phonons) in nuclear matter. We extend this framework to address the dark sector: we propose that both dark matter and dark energy originate as residues of the QCD phase transition at T_c ≈ 156.5 MeV. Dark matter is identified with multi-glueball bound states — the unique GCC-compatible candidate after a systematic exclusion of all Standard Model and beyond-Standard-Model particles, which lack either QCD substructure or a spin-2 quadrupole channel. The relic abundance Ω_gb h² naturally matches the observed Ω_DM h² ≈ 0.12 for formation fractions f_gb ∼ (1—10) × 10u207bu2076 across three mass windows (m_gb ≈ 0.78—2.4 GeV). Dark energy arises from the residual uncondensed fraction (1 − ε) ∼ 10u207bu2074u2075 of the spin-2 condensate energy. While this value is accommodated within the non-linear saturation framework, its precise first-principles pre—diction remains an open theoretical challenge; it constitutes a well-defined target for future development of the saturation dynamics. We show that the Landau parameter Fu2082 reaches −4.97 ± 1.25 (phenomenological estimate) or −3.65 ± 0.41 (conservative RPA with realistic nuclear forces), both approaching the Pomeranchuk instability thresh—old Fu2082 = −5 with critical density n_c/nu2080 ≈ 1.0—1.2. Finite-temperature enhancement mechanisms at the QCD crossover provide the bridge to the threshold. The framework yields falsifiable predictions including a single nanohertz GW peak (5—15 nHz), distinctive 21-cm power spectrum suppression, and CMB lensing signatures, linking the dark sector to ongoing experiments without introducing new particles or energy scales beyond QC.
Category: Relativity and Cosmology
[23] ai.viXra.org:2608.0025 [pdf] submitted on 2026-08-08 01:25:44
Authors: Arūnas Ostasevičius
Comments: 8 Pages.
This paper performs a systematic deconstruction of the electromagnetic field vector reduction originally executed by O. Heaviside and J. Gibbs. We demonstrate that the forced nullification of the Maxwellian field scalar potential S = Real(DA) = 0 deprived the physical vacuum of its fundamental property of volumetric compressibility. Within the proposed framework, the electron is modeled as a deterministic, non-linear quaternionic vortex structured within a dynamic medium of vacuum bubbles (the Wheeler field), stabilized by a Van der Pol attractor under the governance of the quaternionic Virial theorem. A modified energy-momentum tensor (EMT) incorporating a scalar term S^2 is derived, which inherently generates an internal compensating hydrostatic pressure. Operating upon Verhulst-type non-linear logistic equations, it is revealed that the vacuum scalar pressure gradient acts as the fundamental accelerating force of autowave drift (inertia). Concurrently, the cubic non-linear term completely eliminates infinite electronic energy divergences as the core radius approaches zero. Finally, a comparative numerical analysis is provided, demonstrating the physical inadequacy of the classical skin-effect framework traditionally used to dismiss the Tesla-Meyl longitudinal wave transmission experiments.
Category: Quantum Physics
[22] ai.viXra.org:2608.0024 [pdf] replaced on 2026-09-09 04:50:22
Authors: Michael Quigley
Comments: 49 Pages. Restores missing Section 2 (The Standard Model: The Dimensionless Ghost). Seats the 2026 Watts-Mead "Academic Shield" validating 400x scale-invariance across 26 orders of magnitude. Reconciles the 100 pm electron chassis with the 4.244 pm Lund nozzle
This paper performs a trilateral forensic audit of the electron’s physical footprint, resolving the conflict between the Standard Model’s point-particle ghost (0 pm), Jeff Yee’s software blueprint (0.0028 pm), and the Zenodo Wave Model's (4.244 pm) active nozzle. By deploying the "Rocket Analogy," we reconcile these disparate scales, identifying the 100 pm structural body anchored to the 53.0 pm Bohr Radius and the 4.244 pm active machining nozzle captured by the 2008 Lund University attosecond film. This audit now incorporates the 2026 Watts-Mead 'Academic Shield,' providing an independent mathematical description of the Transactional Handshake required for lossless energy transfer. By reconciling the Watts-Mead transition time (τ) with R.U.T. Lattice Setup Time (Ls), we identify the 100 pm chassis as the physical 'tight-fit' assembly that occupies the entire orbital slot, replacing the 'empty atom' of mainstream physics with a singular, phase-locked mechanical instrument. We reclassify the Planck Length (1.6×10−23 pm) as Acoustic Interaction Lag rather than a hardware gear, identifying the 1.0 pm Ether Granule as the "One Ruler" of reality. This resolution unmasks the electron as a precision-machined industrial engine, concluding the century-long retreat into non-predictive mathematical ghosts.
Category: Quantum Physics
[21] ai.viXra.org:2608.0023 [pdf] submitted on 2026-08-08 01:16:04
Authors: Arūnas Ostasevičius
Comments: 5 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
This paper establishes the complete static, geometric, and interference framework of classical field theory by abandoning the stochastic concept of "quantum spacetime foam" in favor of a deterministic elastic medium of vacuum bubbles (the Wheeler substrate). By restoring the Maxwellian field scalar potential S = Real(DA) != 0, previously excised by the Heaviside vector reduction, we derive the fundamental laws of Gauss, Coulomb, and Compton as direct hydrodynamic consequences of phase coupling and volumetric conservation within a compressible cell matrix. Utilizing non-singular cardinal sine distributions (+/-sinc(x)), the mathematical infrastructure of Coulomb interactions is stripped of point-like vector infinities at the core. Physical forces are reinterpreted as localized holographic interference figures: single charges in a state of rest maintain spherical structural symmetry, whereas approaching like charges generate steep spatial compression "spikes" (+1) leading to repulsion, and opposite charges achieve a complementary "lock-and-key" phase locking forming an interference "hole" (-1) resulting in external hydrostatic attraction. Finally, the Compton effect is rigorously mapped not as particle scattering in a void, but as a non-elastic mechanical collision between a propagating autowave packet of micro-bubbles and the rotating boundary of a macro-bubble core, validating the structural perimeter of the electronic vortex without invoking Planck’s constant.
Category: Quantum Physics
[20] ai.viXra.org:2608.0021 [pdf] submitted on 2026-08-07 22:46:14
Authors: E. P. J. de Haas
Comments: 58 Pages. https://doi.org/10.5281/zenodo.21844437
The empirical Constant-Lagrangian (CL) relation has previously been shown to reproduce a substantial fraction of observed galactic rotation curves, but until now it has lacked a theoretical foundation. This paper derives the CL condition from a gravitational rapidity field that generates a local Spin(1,3) rotor describing the vacuum flow surrounding a galaxy.Two independent but complementary geometric branches emerge from the same gravitational rotor. The first is a kinematic branch, in which the rapidity field generates the gravitational four-velocity and its convective acceleration. The second is a Maurer—Cartan branch, in which the differential geometry of the rotor itself is described through its Lie-algebra-valued connection. Although these branches describe different geometric objects, both converge on the same invariant isorapidity condition, expressing the conservation of the combined radial and azimuthal rapidity along the flow. In the weak-field limit, this invariant reduces directly to the Constant-Lagrangian relation governing the exterior galactic rotation curve.The construction is developed in its native BQ (biquaternion) algebra and subsequently translated into three standard mathematical languages: the Weyl representation of Clifford algebra Cl(1,3), Spacetime Algebra, and the conventional Dirac spin formalism. The agreement between these independent formulations demonstrates that the resulting isorapidity condition is a representation-independent consequence of the underlying Spin(1,3) rotor geometry rather than an artifact of a particular algebraic framework.Beyond providing a theoretical basis for the empirical Constant-Lagrangian postulate, the paper presents a unified rotor-based description in which both the kinematics of galactic vacuum flow and its Maurer—Cartan transport originate from the same gravitational rapidity field.
Category: Relativity and Cosmology
[19] ai.viXra.org:2608.0020 [pdf] submitted on 2026-08-05 18:09:44
Authors: Lluis Eriksson
Comments: 17 pages. Lean 4 formalization. AI-assisted with OpenAI Codex; all Lean builds and axiom-oracle checks were verified by the author. Source and validation evidence are linked in the PDF.
We present a Lean 4 formalization of a thermodynamic-limit construction for the anisotropic nearest-neighbour Ising model on the two-dimensional integer lattice. A telescoping comparison argument and the classical Dobrushin resolvent produce a volume-uniform expectation bound. Exact restriction and reindexing maps between finite Gibbs measures yield convergence of the complete free-boundary sequence, independence of auxiliary envelopes and cofinal samplings, stability under receding boundary perturbations, and equality of free and periodic limits.Finite-support cylinder presentations are quotiented by equality of their represented functions on the full spin space. The resulting local algebra carries a genuine lattice-translation action, and the limiting functional is positive, normalized, real-linear, and invariant under every integer translation. We equip this algebra with its intrinsic uniform norm, construct its complex star-algebra representation, take the corresponding commutative C*-closure, and extend the limiting functional to a positive complex-linear functional of norm one. We also formalize normalized Gibbs conditional kernels for arbitrary finite conditioning sets and prove positivity, exterior locality, idempotence, and the exact finite-volume Gibbs tower identity.All results remain within the classical anisotropic Dobrushin region. The infinite-volume DLR fixed-point equation for the completed state is not claimed.
Category: Mathematical Physics
[18] ai.viXra.org:2608.0019 [pdf] submitted on 2026-08-05 18:19:22
Authors: Lluis Eriksson
Comments: 31 pages, 1 figure. Companion reproducibility archive containing complete LaTeX source, numerical verification code, data and SHA-256 manifest.
We determine when rapid exact maintenance of a rank-deficient quantum target produces logarithmically divergent free-energy restoration power in algebraic quantum field theory. On every sigma-finite properly infinite factor we construct a bounded quantum Markov semigroup, a nonfaithful normal target and a faithful invariant reference state for which Araki relative entropy reduces exactly to a binary divergence. We derive the semigroup first from localized thermal fermionic probe collisions and then from one autonomous finite-bandwidth Dirac KMS reservoir with fixed smooth coupling. Exact memory equations yield an explicit finite-coupling Davies bound on finite van Hove windows. For a displayed compactly supported massless Dirac form factor, Araki—Wyss regularity, threshold behaviour and Fermi-golden-rule positivity give a completely bounded Davies approximation uniformly for all times with error of order (O(|lambda|)); the sharper (O(lambda^2)) result is isolated under additional reduced-resonance hypotheses. We construct a background-covariant two-Dirac-field completion using Green operators, Møller maps and relative Cauchy scattering, proving naturality, causal factorization and exact spacelike triviality. A locality obstruction shows why a strictly local multiplier cannot coincide exactly with the solvable rank-one reservoir coupling, while a Feshbach reduction quantifies the correction. Finally, we prove that no fixed faithful vacuum or KMS restriction can exhibit the rank-boundary mechanism, but faithful families with a vanishing spectral floor recover its complete coefficient. The results separate algebra type, target faithfulness, microscopic realizability and regulator uniformity, and provide reproducible numerical audits of the finite-dimensional identities and explicit Dirac form factor.
Category: Mathematical Physics
[17] ai.viXra.org:2608.0018 [pdf] submitted on 2026-08-05 21:39:01
Authors: Lluis Eriksson
Comments: 13 Pages. All results are machine-checked in Lean 4 (no sorry, no project axioms; headlines depend on exactly [propext, Classical.choice, Quot.sound]).
For the spatial Z_2 (Ising-slice) system inside the Dobrushin window 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1, we machine-check in Lean 4 an end-to-end chain from the Gibbs measure to the spectrum of the reconstructed transfer operator. (i) The Osterwalder-Schrader (site-form) reconstruction of the transfer operator is unitarily conjugate, by the explicit sqrt(w) boundary dressing, to the symmetrised Dobrushin kernel. (ii) The unnormalised Gibbs sums themselves are exact matrix elements of that operator's powers: gibbsPathSum(w,beta,N,A,B) = lambda^N
Category: Mathematical Physics
[16] ai.viXra.org:2608.0017 [pdf] submitted on 2026-08-04 14:28:32
Authors: Joseph Palazzo
Comments: 10 Pages.
The universe is causally connected at all scales, but at microscopic scales the total causal network is fundamentally inaccessible. These irreducible epistemic limits are themselves ontological features of reality. Classical determinism emerges gradually as systems increase in scale, making the inaccessible fraction of causal information negligible.
Category: History and Philosophy of Physics
[15] ai.viXra.org:2608.0016 [pdf] submitted on 2026-08-04 19:14:39
Authors: Lluis Eriksson
Comments: 9 pages. New companion obstruction paper to ai.viXra:2607.0089, not a replacement. Diagnostic code and reproducibility record: https://github.com/lluiseriksson/THE-ERIKSSON-PROGRAM
For beta > 0 let I_m = I_m(beta) denote the modified Bessel functionof the first kind and define a_m = I_m^2 ((m-1) I_(m-1)^2 + (m+1) I_(m+1)^2), b_m = m I_m^4,with sine series F_A(t) = sum_(m>=1) a_m sin(mt) andF_B(t) = sum_(m>=1) b_m sin(mt). The associated Wronskian is negativeexactly when F_A/F_B is decreasing. We isolate what can and cannot beproved from two natural inputs: the Neumann convolution kernelI_0(2 beta sin(phi/2)) and the small-coupling anchor whose normalizedlimit is 4 sin^3(t).First, the convolution does prove F_B(t) > 0 for 0 < t < pi. Second,the endpoint is governed by two alternating quantities, c_3 and B_pi,through an exact cubic law. We prove B_pi > 0, derive integralrepresentations, and establish that the cancellation lost by replacingthe alternating quantities with positive-term majorants has exponentialrate 8 - 4 sqrt(2). Finally, we prove a smooth one-parameter perturbationtheorem: one may keep F_B and its kernel unchanged, preserve positivityand strict coefficient-ratio ordering, and preserve every jet at beta = 0,while choosing either sign of the endpoint cubic coefficient.Consequently those structural data, even taken together, do not implyglobal Wronskian negativity. This is a no-go theorem for a proofarchitecture, not a counterexample to the original Bessel conjecture.A short high-precision kill-test accompanies the paper; nocomputer-assisted inequality is used in the proofs.
Category: Mathematical Physics
[14] ai.viXra.org:2608.0015 [pdf] submitted on 2026-08-04 19:42:27
Authors: Lluis Eriksson
Comments: 13 Pages.
We study whether a flat lattice-gauge Hodge form supplemented by a penalty depending only on a line-integral block variable can control the full fine one-cochain norm uniformly in the block side. The constant-field sector selects the exponent (d-2)/2 only under exact scale neutrality, but this scaling test does not address the kernel of the block map. We construct transverse, divergence-free, block-periodic Fourier cochains that are annihilated exactly by the block map. Their first-mode Hodge Rayleigh quotient is 4 sin²(pi/L), forcing every admissible full-space Poincaré constant to grow at least quadratically with L. The obstruction applies to every scale-dependent scalar functional factored through the block variable and satisfying only that it vanishes at the coarse zero field; no linearity, continuity, positivity, or growth condition is required. For linear postconditioners, higher Fourier frequencies yield an orthogonal real subspace of dimension 2R and a min—max bound on the 2R-th eigenvalue, establishing a growing low-energy spectral cluster. We also derive an exact repair identity and a necessary witness-channel budget for modified block measurements and additional fine-space terms. The kernel construction, Hodge energy, factorized no-go theorem, repair identity, and necessary repair budget are formalized in Lean 4. The result concerns a finite periodic flat full-domain form and makes no claim about interacting coercivity, gauge quotients, continuum limits, or the Yang—Mills mass gap.
Category: Mathematical Physics
[13] ai.viXra.org:2608.0014 [pdf] submitted on 2026-08-03 17:55:12
Authors: Brent Hartshorn
Comments: 6 Pages. https://github.com/brentharts/crust/
We present Crust, a self-hosted compiler that accepts C, a subset of C++, a subset of Rust and a subset of rpython in a single translation unit, together with its own assembler, linker, freestanding runtime and operating system. After bootstrap the chain depends on no external toolchain: not GCC, not LLVM, not GNU as or ld, and not a host libc. The system is deliberately kept small enough that its entire call graph fits in the context window of a large language model, and we argue this constraint is what makes a system auditable in an era when the reader is increasingly a machine. As a worked example we take the removal of a layer usually treated as part of the machine — the return-address stack — and, with archived and reproducible measurements [20], show both a two-order-of-magnitude pitfall in the naive implementation and a regime in which abandoning the stack is faster than the hardware’s own return predictor. The point of the example is not the speed but the epistemics: the pitfall, the fix, and the regime were each found, made, and checked inside a toolchain small enough to read whole.
Category: Data Structures and Algorithms
[12] ai.viXra.org:2608.0013 [pdf] replaced on 2026-08-04 10:13:23
Authors: Lluis Eriksson
Comments: 25 pages. Lean 4, no sorry, no project axiom. Twelve machine-checked theorems: positive weight to exponential decay, and through an abstract transport theorem to a volume-uniform operator gap.
A formal Lean 4 development revisits a two-dimensional spatial transfer kernel whose earlier uniform spectral argument relied on constant row sums. We show that the loss of row-sum constancy obstructs that method, not the conclusion. With no sorry and no project axiom, we prove twelve machine-checked theorems.The chain establishes the sharp field-uniform one-bond influence envelope tanh J; assembles these bounds into a finite-volume Dobrushin matrix; proves a volume-independent resolvent estimate under row-sum bounds alpha < 1 without assuming constant rows; mechanises Dobrushin's comparison inequality with the attained 1/4 covariance constant; constructs Gibbs measures, heat-bath kernels and intrinsic influence matrices from arbitrary strictly positive finite weights; and specialises to anisotropic Ising interactions. For L x T rectangles with free boundary, the condition 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1 yields exponential decay of correlations with beta, gamma, alpha and the prefactor fixed before the volume quantifiers.The transport into the operator formulation is closed: an exact finite band identity relating endpoint covariances to matrix elements; an abstract theorem showing that a common exponential decay rate for band covariances - a hypothesis on finite path measures, carrying no operator, norm or spectrum - implies a uniform positive gap for a family of projected transfer operators; a Perron-boundary tilt identity that preserves the decay rate while absorbing boundary costs into extent-dependent constants; an exact currying identification of the free strip measure with the rectangle Ising measure; and the resulting corollary: inside the window there is one m > 0 bounding the projected transfer operator of the coupled kernel's normalised Perron data by exp(-m) at every extent, with m = -log alpha.Numerical measurements at L <= 12 provide counterevidence to attributing spectral degeneracy solely to nonzero spatial coupling. No infinite-volume state, thermodynamic limit or boundary-condition independence is constructed; the window is sufficient, not sharp. The underlying Dobrushin mathematics is classical; the contribution is a non-vacuous, reproducible mechanisation and composition of the full chain, ending at a volume-uniform operator gap. No consequence for Yang-Mills theory is claimed.
Category: Mathematical Physics
[11] ai.viXra.org:2608.0011 [pdf] submitted on 2026-08-02 02:41:29
Authors: Charles A Streb IV
Comments: 15 Pages.
This is an expository reference on the mathematical structure of quantum entanglement.It contains no new results. Part I treats the nite-dimensional theory, where entanglement isdened by the failure of a convex tensor decomposition and is computable in principle. PartII treats the innite-dimensional and algebraic setting. For sharp local regions in relativisticquantum eld theory, the tensor-product and reduced-density-matrix framework generally fails:under the usual phase-space and scaling assumptions, local observable algebras are typicallyhypernite factors of type III1, with no intrinsic normal seminite trace, no intrinsic localdensity matrix, and no reduced-state von Neumann entropy. Part III develops the structuresthat replace that framework TomitaTakesaki modular theory, Araki relative entropy, and thecrossed-product construction. The continuous core of a type III1 factor is type II∞ and carriesa seminite trace; in the gravitationally dressed de Sitter observer construction, the resultingobservable algebra is type II1. Statements are proved when the proof is short and otherwiseattributed precisely. The intended use is as a denitional reference: every term is pinned, andevery substantive claim is either proved here or tied to a cited result with its hypotheses stated.
Category: Quantum Physics
[10] ai.viXra.org:2608.0010 [pdf] submitted on 2026-08-02 03:33:12
Authors: Lluis Eriksson
Comments: 8 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib 07642720480157414db592fa85b626dafb71355b. Clean rebuild passed. 25 public declarations; no sorry, admit, or local axiom. New sequel, not replacement; four-face crossing not claimed.
We give a kernel-checked positive-area calculus for the concrete SU(2) classheat kernel used in two-dimensional Yang—Mills theory. With irreducible labeln, dimension n+1, and Casimir c_n=n(n+2)/4, Lean verifies at every positivetime and every derivative order that the infinite spectral jet converges anddifferentiates term by term to the next jet. The hierarchy is packaged as aC-infinity map on the positive-time half-line, using explicit uniform summablemajorants on positive-time neighbourhoods. We then differentiate the literalnormalized-Haar two-face Migdal integral, prove that its left and right areaderivatives equal the first spectral jet at the merged area, and showinfinitesimal invariance under (s,t) -> (s+u,t-u). Finally, every normalizedWilson character satisfies its exact Casimir area ODE as an actual Haarintegral against the infinite heat kernel. The artifact contains 25 publicdefinitions and theorems, no local placeholders, and audited dependencies onlyon propext, Classical.choice, and Quot.sound. We do not claim the four-faceMakeenko—Migdal crossing equation; the remaining inputs are local Lie-groupintegration by parts and certified crossing geometry.
Category: Mathematical Physics
[9] ai.viXra.org:2608.0009 [pdf] submitted on 2026-08-02 07:14:51
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 30 public declarations; no sorry, admit, or local axiom.
We formalize the finite-dimensional integration-by-parts mechanism used inlocal proofs of the Makeenko—Migdal equation. For a measure-preserving realflow on a finite measure space, Lean verifies differentiation under theintegral from an explicit locally uniform integrable majorant and proves thatthe integral of the generator vanishes. A bounded dominated product interfacethen yields integration by parts, and two successive applications transfer amixed pair of generators from a density to an observable with positive sign.These results are instantiated on normalized Haar probability measure ofconcrete SU(2) and on every finite product SU(2)^E, for left and rightmultiplication of one selected edge. To fix the representation normalization,we construct three explicit trigonometric curves in SU(2) and prove entrywisethat their tangents at the identity are i sigma_1/2, i sigma_2/2, and isigma_3/2. The producer contains 30 public definitions, structures, andtheorems in 519 physical lines; its audit contains no local sorry, admit, oraxiom, and the headline results depend only on propext, Classical.choice, andQuot.sound. This closes the Haar integration-by-parts layer. It does not claimthe full four-area Makeenko—Migdal identity: the remaining formal inputs arethe heat-density directional identity, extended gauge invariance at acrossing, and their geometric assembly.
Category: Mathematical Physics
[8] ai.viXra.org:2608.0008 [pdf] submitted on 2026-08-02 11:55:22
Authors: Lluis Eriksson
Comments: 18 pages. All new lemmas machine-checked in Lean 4 (pinned Mathlib); the supremum theorem is conditional, carrying the Birkhoff spectral bound as an explicit hypothesis, not an axiom. Source: github.com/lluiseriksson/THE-ERIKSSON-PROGRAMME
A positive site weight acts on a transfer kernel by congruence, K -> DKD with Dpositive diagonal, not by similarity. Similarity preserves the entire spectrum;congruence preserves strictly less, and strictly more than nothing. We determineboth halves for the kernel of L decoupled Ising bonds. Rigid half: the sign ofevery quadratic form value survives, so definiteness in either sign is acongruence invariant -- the definite case of Sylvester's law of inertia, in aform a machine can check without diagonalisation. Fragile half: the subdominantratio r (second eigenvalue modulus over the Perron root) does not survive atall, and we locate exactly how far it moves. Restricting the L-site kernel tothe two antipodal configurations leaves one Ising bond of coupling bL, of ratiotanh(bL) for b>0: a weight concentrating there fuses the L sites into a singleeffective site carrying L times the coupling. Since tanh(bL) -> 1, no boundr <= rho < 1 holds simultaneously in L and over the whole positive-diagonalcongruence orbit; the obstruction to volume-uniformity is a property of thecongruence, not of any spectral estimate, so an argument bounding r throughcongruence invariants alone cannot produce an L-uniform bound. For arbitraryweights we prove sup_{D>0} r(DMD) = (1-m)/(1+m), where m is the leastoff-diagonal entry: the least correlated pair determines the supremum. (Weevaluate the supremum; we do not classify its maximisers.) The proof isgeometric rather than spectral -- Hilbert's projective diameter is itself acongruence invariant, and Birkhoff's contraction theorem converts it into thebound -- and uses no definiteness, only positivity of the entries. The lowerbound uses no limiting argument about spectra: a two-supported fluctuationvector gives the estimate at each strictly positive epsilon, so no continuity ofeigenvalues is imported anywhere.
Category: Mathematical Physics
[7] ai.viXra.org:2608.0007 [pdf] submitted on 2026-08-02 14:02:27
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 1 figure. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 19 public declarations; no sorry, admit, or local axiom.
We formalize a finite-dimensional crossing Ward identity for fundamental SU(2) Wilson words. On every finite edge space SU(2)^E, two distinct coordinates are inserted into a concrete normalized trace word. Lean proves entrywise that right multiplication by each of three explicit SU(2) curves produces the normalized Pauli generators i sigma_a/2, differentiates the trace word once at each selected coordinate, and identifies the Pauli-summed mixed derivative with the rank-two Fierz contraction. Two applications of Haar integration by parts transfer the corresponding mixed generators from a density to the Wilson word. The resulting integral closes exactly on the direct and reverse single-trace resolutions, with coefficients -1/4 and -1/2 in the chosen normalization. The producer contains 19 public declarations in 487 physical lines; all 13 new theorems depend only on propext, Classical.choice, and Quot.sound, with no local sorry, admit, or axiom. This is not a full Makeenko--Migdal area equation: the remaining physical input is a weak four-face identity against crossing-certified extended-gauge-invariant observables. In the program's heat time, generated by the Pauli Laplacian, its coefficient is kappa = 2.
Category: Mathematical Physics
[6] ai.viXra.org:2608.0006 [pdf] submitted on 2026-08-02 16:46:30
Authors: Lluis Eriksson
Comments: 6 pages, 2 tables, 2 figures. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 56 public declarations; no sorry, admit or local axiom.
We formalize extended gauge invariance at a simple four-edge SU(2) crossing and connect the geometric edge chart to the two-coordinate chart used by a machine-checked crossing Ward identity. On SU(2)^4 we define the two opposite-edge right actions from the abstract Makeenko--Migdal theorem, prove that they are commuting product-Haar-preserving actions, and show that their common parameter composes to ordinary vertex gauge invariance. The four-edge Wilson word tr2(a3^-1 beta a2 a4^-1 alpha a1) is proved invariant under both half-actions. We construct the explicit quotient r(a)=(a2 a4^-1,a1 a3^-1), a canonical section, and prove existence and uniqueness of the universal factorization for every extended-gauge-invariant complex function. The complete map from the cyclic four-edge chart to physical and gauge coordinates is proved to preserve literal four-fold Haar measure in one public endpoint. Finally, the four-edge Wilson word is identified exactly with the prior two-coordinate crossing word evaluated on r(a). The Lean producer has 56 public declarations in 488 physical lines; all 36 theorems depend only on propext, Classical.choice, and Quot.sound, with no local proof escape. No heat-kernel area derivative or full Makeenko--Migdal equation is claimed.
Category: Mathematical Physics
[5] ai.viXra.org:2608.0005 [pdf] submitted on 2026-08-02 19:16:06
Authors: Lluis Eriksson
Comments: 7 pages, 2 tables, 2 figures. Lean 4.29.0-rc6; Mathlib commit 07642720480157414db592fa85b626dafb71355b. Clean-source build and audit passed. 26 public declarations; no sorry, admit or local axiom.
We machine-check the exact measure and differential bridge between thefour-edge SU(2) crossing chart and the two effective group coordinates used bya finite-dimensional Ward identity. The quotientr(a)=(a2 a4^-1,a1 a3^-1) pushes normalized four-fold Haar measure exactly tonormalized two-fold Haar measure. Two gauge-compensated flows on the originalfour edges intertwine with independent right multiplication of the quotientcoordinates, so first and mixed derivatives of the crossing Wilson worddescend without choosing a gauge. The three Pauli directions are verifiedindividually, their mixed generators close into direct and reverseresolutions, and the two-coordinate Ward theorem lifts to a literal four-edgeintegral with coefficients -1/4 and -1/2. This compensated operator is notidentified with the ordinary-edge mixed operator of Driver-Hall-Kemp: thepaper writes both operators and their distinct reverse resolutions and markstheir comparison as open. The Lean producer has 26 public declarations and 16audited theorems. No weak four-face heat-kernel identity, area derivative, orfull Makeenko--Migdal equation is claimed.
Category: Mathematical Physics
[4] ai.viXra.org:2608.0004 [pdf] submitted on 2026-08-02 19:25:02
Authors: Lluis Eriksson
Comments: 8 pages. Lean 4 formalization with pinned Mathlib. Nine headline declarations were audited and depend only on propext, Classical.choice, and Quot.sound; no project axioms or sorryAx. Formal source frozen at commit f21539ed0bb880a04078de369bf5cbf063f7b101.
Let a fine periodic lattice have side LN' and let Q_L be the L^{-d}-normalized block average of length-L line integrals. In four dimensions, the rescaling Q_L -> LQ_L repairs the elementary constant-field scaling obstruction to a Poincare estimate. We prove that it cannot yield coercivity on the full one-cochain space with a constant uniform in the block side.For every L >= 2, every fixed N' >= 1, and N_c >= 2, we embed the first within-block Fourier phase zeta_L = exp(2 pi i/L) in a real two-plane of the internal coordinate space and construct a transverse one-cochain A_L. It satisfies Q_L A_L = 0 and div A_L = 0. For every dimension d >= 2,||A_L||^2 = (LN')^d,
Category: Mathematical Physics
[3] ai.viXra.org:2608.0003 [pdf] submitted on 2026-08-01 23:42:12
Authors: J. W. McGreevy
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)
We develop a symplectic geometry of atomic shear measures supported on the irregular primes of a modular curve. Starting from a space of dis-crete measures subject to a global valence constraint, we perform a strict symplectic reduction and obtain a reduced phase space equipped with a canonical Darboux form. The local coordinate functions that extractthe individual shear amplitudes are shown to be in Liouville involution, generating a completely integrable system whose invariant level sets areLagrangian tori. By lifting the functional equation of the associated automorphic L-functions to an anti-symplectic involution on this phase space, and under the established essential self-adjointness of the clutched conical Dirac operator, we prove a Confinement Theorem: the only invariant Lagrangianleaves compatible with the reflection symmetry are those whose spectralimage lies on the critical line Re(s) = 1/2. We conclude with a brief, explicitly programmatic dictionary that explores possible links between the resulting arithmetic geometry and structures appearing in gauge theory and the Standard Model. This workextends earlier constructions developed under the working title Relativistic Field Theory of Primes (RFTP), in which the irregular primes, the weight-12 valence constraint, and the associated clutching data were first introduced as geometric ingredients of an arithmetic field theory.
Category: Mathematical Physics
[2] ai.viXra.org:2608.0002 [pdf] submitted on 2026-08-01 23:35:07
Authors: Nigel B. Cook
Comments: 9 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
It is shown that SU(4) and SL(4,R) both offer feasible alternative routes to unification, justifying the twistor unification approach and therefore getting rid of superstring theory. Paper was proof read by Copilot AI to check maths.
Category: Quantum Gravity and String Theory
[1] ai.viXra.org:2608.0001 [pdf] submitted on 2026-08-01 18:50:53
Authors: Lluis Eriksson
Comments: 9 Pages. Lean 4/Mathlib formalization of the finite-SU(2) Pauli/Casimir contraction, trace-skein identity, four oriented local branches with both reconnections, corrected single-crossing closure, and an all-order multitrace-to-single-trace recursion.
Finite-rank Makeenko-Migdal equations generate products of Wilson traces at self-intersections. For SU(2), this apparent multitrace obstruction closes exactly on single traces, but the statement is normalization-sensitive: the traceless Lie algebra contributes a finite-rank correction that disappears for U(2) and must not be dropped. We give a Lean 4/Mathlib formalization of the complete group-algebraic closure mechanism on Mathlib's concrete special unitary matrix group. With normalized trace tau(A)=Tr(A)/2 and normalized anti-Hermitian Pauli directions X_j=i sigma_j/2, the kernel checks the Casimir identity, the rank-two Fierz identity, the induced crossing contraction, and the SU(2) trace-skein identity tau(g)tau(h)=(tau(gh)+tau(gh^{-1}))/2. Consequently, the finite-SU(2) crossing term tau(g)tau(h)-tau(gh)/4 equals tau(gh)/4+tau(gh^{-1})/2. We then formalize a universal local interface with four cyclically ordered branch holonomies, an independent orientation on each branch, the two opposite-strand words, and precisely the two direct/reversed reconnections. Its corrected crossing term closes on those reconnections for every branch assignment and orientation choice. A recursive theorem also extends the reduction to products of arbitrarily many fundamental traces. The identities are classical; the contribution is a concrete, kernel-checked normalization bridge from Pauli contraction to the single-trace closure used in finite-rank loop equations. We do not claim a formal derivation of the Yang-Mills area derivative, planar loop geometry, or the full Makeenko-Migdal equation.
Category: Mathematical Physics