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[6] 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
[5] 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
[4] 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
[3] 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
[2] 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
[1] 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