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[7] ai.viXra.org:2604.0103 [pdf] submitted on 2026-04-30 13:33:27
Authors: Jason Merwin
Comments: The document contains 12 pages. A link to the code repository is provided.
A prior distinction-engine construction recovered a 137-object registry at DAG size 7 and partitioned it into sectors of 81+40+16, aligning with the spatial, interface, and gravitational sectors proposed in Relational Mathematical Realism. The present manuscript consolidates two subsequent analyses. First, we study mature registry carriers: larger relational objects that contain the full 137-type registry as an embedded motif. Exact DAG-size joins and 137-bit registry signatures recover DAG-8, DAG-9, and DAG-10 layers while compressing motif state space by factors of 6.85x, 20.43x, and 46.01x. Minimal full-registry carriers have DAG size 309. Eight non-isomorphic carrier histories preserve the same condensable typed mediation geometry: 72 spatial nodes, 38 interface nodes, 16 gravitational nodes, and 288 mediated S-G edges per condensable interface node. Typed dynamics lifted onto these mature carriers show no statistically detectable topology effect on interface-enabled condensation. A screening audit identifies full binary S-G conflict deletion as the wild-type interface rule, producing S_ DYN ~9.61, S_OFF~2.04, and a 4.73x dynamic/OFF enhancement. Loss-of-function tests identify the true invariant as complete I-mediated coverage of the active S-G conflict graph: the 38 condensable I nodes split into two complementary 19-node half-covers, each covering 288 of 576 active S-G edges.Second, we extend the analysis to an open-token distinction engine, in which finite type identity is separated from lineage-distinct token identity. The type-guarded open-token process preserves the canonical 137 DAG-7 type layer exactly while allowing unbounded token multiplicity. Particle-detector tests on open-token dynamics recover robust K3/baryon-like candidates: five stable candidates with k3_score=1.0, high closure, and fixed carrier support. I-cage/lepton-like structures appear as suggestive precursors, including a high-scoring cage-localized candidate, but not yet as fully closed localized leptons. These results support a layered interpretation: the DAG-7 registry is a finite reusable type grammar; DAG-309 carriers are mature local embeddings of that grammar; and open-token dynamics permit stable particle-like excitations over repeated registry instances. We identify a mathematically natural route from distinction-generated registry types to mature carriers and K3-centered particle-like object.
Category: Mathematical Physics
[6] ai.viXra.org:2604.0090 [pdf] submitted on 2026-04-27 09:13:28
Authors: Zhang Xiangqian, Zhao Mingming, Ge Linchao
Comments: 9 Pages.
This paper aims to construct a unified framework between discrete number theory, differentialgeometry, and continuous quantum physics through the "Topological Residual Theory." The researchtakes the 19th term of the Fibonacci sequence (Fu2081u2089 = 4181) as the core node. First, it reveals itsmathematical miracles in semiprime decomposition and fractal dimension reduction. Subsequently,this paper completely derives the differential geometric correspondence between the Binet residualand the torsion of the cylindrical helix, and details the calculation of the torsion limit (τ → 1/3) of theMarkov triples related to 4181. From first principles, it rigorously proves that this node defines theglobally stable geodesic line on the torus with no self-intersection and minimum energy.Furthermore, this paper introduces renormalization group scale transformation, dividing theFibonacci sequence by ten thousand (10u2074) and extracting its sine value, mapping it as the transverseperiodic projection of cylindrical spiral motion. Through key transition data tables and visualizationcharts, this paper intuitively demonstrates the physical mechanism by which the macroscopictopological node 4181 still maintains the minimum energy ground state after being scaled down byten thousand times (0.4181°). It proves that the fine structure constant (α ≈ 1/137) is essentially themicroscopic transverse geometric projection residual (sin(0.4181°) ≈ α) that maintains the cylindricalhelix moving at the limiting velocity u without collapsing, and that Fu2081u2089 holds an absolutelyirreplaceable critical phase transition position in the evolutionary cycle. Finally, this paper proposesthat the space around objects is structured on the basis of right-handed cylindrical spiral motion,providing solid geometric and dynamic support for the holographic universe principle
Category: Mathematical Physics
[5] ai.viXra.org:2604.0080 [pdf] submitted on 2026-04-24 19:22:58
Authors: Hao Gui
Comments: 24 Pages. This submission uses the CC BY-NC-ND 4.0 International License.
We rigorously prove that pure SU(N) Yang—Mills theory (N ≥ 2) on R^4 exists and has a positive mass gap Δ > 0. This paper presents the second of six independent proofs, centered on the analytic properties of the lattice partition function. The non-negativity of the Wilson action (S_W ≥ 0) implies, via the Bernstein—Widder theorem, that Z(β) is the Laplace transform of a positive measure, hence completely monotone and holomorphic in the entire right half-plane {Re β > 0}. This elementary observation has profound consequences: (i) Z(β) > 0 for all real β > 0 (no Lee—Yang zeros on the physical axis); (ii) the free energy f(β) is real-analytic, concave, and has a continuous derivative (excluding first-order transitions); (iii) combined with β < 0 at all couplings (proved via operator positivity and Lorentz algebraic protection), the theory has no phase transitions of any kind, and the mass gap propagates continuously from strong to weak coupling. The holomorphicity of Z provides the strongest possible regularity for the coupling dependence, making gap propagation a consequence of complex analysis rather than operator theory.
Category: Mathematical Physics
[4] ai.viXra.org:2604.0061 [pdf] submitted on 2026-04-16 16:30:36
Authors: Xiangqian Zhang, Mingming Zhao, Linchao Ge
Comments: 7 Pages.
Modern physics has long faced the dilemma of unifying quantum mechanics and general relativity, and theStandard Model contains numerous free parameters that cannot be derived from first principles. Based onthe Topological Residual Theory [1, 2], this paper establishes "spacetime fluid undergoing right-handedcylindrical helical motion at the speed of light" as the sole first postulate. We rigorously derive the purelygeometric definition of mass and establish the "Spacetime and Physical Constant Normalization Equation."Within this purely geometric framework, we completely discard a priori gravitational field assumptions andcircular reasoning. Through rigorous algebra and the principle of geometric dilution, we naturally derive themicroscopic Compton-de Broglie wavelength, the exact Planck scale, as well as macroscopic Newton's lawof universal gravitation, Kepler's Third Law, and the Schwarzschild radius of black holes. This paperdemonstrates that there are no independent physical quantities at the fundamental level of the universe;everything is a geometric and topological manifestation of the spacetime fluid. Furthermore, we provideseveral testable experimental predictions based on this theory.
Category: Mathematical Physics
[3] ai.viXra.org:2604.0057 [pdf] submitted on 2026-04-13 13:51:27
Authors: Jason R Merwin
Comments: The manuscript contains 7 pages
We construct a distinction engine from the minimal axiom A̸ = B applied to two primitives and show that exhaustive iteration produces exactly 137 permanent objects at directed acyclic graph (DAG) size 7, matching the OEIS sequence A255841. Two nested topological cuts on the resulting overlap graph partition these 137 objects into sectors of 81 + 40 + 16, reproducing the registry architecture of Relational Mathematical Realism (RMR) previously derived from complete-graph eigenvalue spectra, force emergence mechanisms, and lepton mass ratios. The partition is unique:varying the number of primitives, DAG size, pairing rules, or overlap threshold destroys it. A heterogeneous dynamical simulator with algebraically typed update rules—ternary condensation (34 = 81), binary polarity (24 = 16), and relational activation (52 × 4 = 40)—produces sector-differentiated behavior with exact energy conservation. Ablation of the interface sector demonstrates that the 40-element boundary enables matter-like condensation: removing it reduces spatial-sector realization by 80% (p < 10−10). The dynamic interface achieves full condensation efficiency with just 2 of 38 channels active, revealing massive structural redundancy and a sharp percolation-likethreshold. Seven of twelve integers in the established RMR set A appear as direct structural counts in the engine; the remaining five appear as derived ratios, including the generation factor 17 = 136/8. This constitutes a fourth independent line of evidence for the RMR registry partition, obtained from pure combinatorics with zero free parameters.
Category: Mathematical Physics
[2] ai.viXra.org:2604.0024 [pdf] submitted on 2026-04-07 19:17:11
Authors: J. W. McGreevy
Comments: 15 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We construct a relativistic field theory of primes (RFTP) in which the adelic phase space is quantized by a single arithmetic object — the motivic commutator arising from the 691 topological defect. The twisted Lorentz oscillator serves as the microscopic foundation, yielding a direct derivation of Planck’s law and the entropy of a single harmonic oscillator from the commutator spectrum, with zeta regularization modulated by the 691 rigidity. The defect, realized as the non-trivial Galois extension forced by the vanishing Stickelberger element when 691 divides B12, functions as a universal cohomological object that factors through all Weil cohomologies. Stationarity of the combined action produces EinsteinCartan geometry as the thermodynamic equation of state describing curvature annealing of the defect until the conductor-9 snag, where octonionic triality locks vertical phase into GL(3) structure, generating rest mass via the Higgs-like clutching mechanism. Photons emerge as the symmetric null limit of the commutator, while massive particles arise from partial or full clutching. The theory recovers Maxwell equations in the low-energy phase, Dirac dynamics with torsional corrections, and entropic gradients driving probability flow. Implications for the BSD conjecture, Hilbert’s 12th problem, Navier-Stokes smoothness, and the Riemann Hypothesis are noted, but formal resolutions are deferred to dedicated manuscripts. The framework offers a first-principles unification of number theory with relativistic quantum field theory and gravity through a single motivic commutator.
Category: Mathematical Physics
[1] ai.viXra.org:2604.0010 [pdf] submitted on 2026-04-03 20:54:40
Authors: J. W. McGreevy
Comments: 17 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We extend the Relativistic Field Theory of Primes by identifying the motivic object at thecentral cusp of the adelic upper half-plane — the non-orientable homology cycle γ pairedwith its divergence-free cohomology current JAudit, under the M¨obius twist correspondenceτ : γ 7→ −γ — as the intrinsic adelic Planck constant ℏA. This single topological object supplies the fundamental unit of action. It quantizes the adelic phase space via the commutator [τ, γ] = iℏAΩ, deforms the constitutive tensors εA and µA, derives the elementary charge eA from the holonomy around the minimal twist loop, and yields the fine-structure constant αA as a pure geometric ratio. Starting from the twisted Lorentz oscillator as the microscopic probe, the theory builds upward: the Bernoulli irregularity at weight 12 (prime 691) sets torsional rigidity, entropy gradientsdrive probabilistic flow, and the resulting entropic force produces Einstein-Cartan geometryas a thermodynamic equation of state (Jacobson-style). The same motivic object that quantizes the adelic phase space also defines the vacuumproperties and the coupling constant, providing a self-contained geometrization in whichclassical spacetime, quantum spin statistics, and Standard Model parameters emerge fromthe fundamental duality between analytic volume and algebraic rigidity.
Category: Mathematical Physics