|
 |
[7] ai.viXra.org:2610.0048 [pdf] submitted on 2026-10-22 21:12:40
Authors: Tomasz Kobierzycki
Comments: 11 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references!)
his paper formulates a purely complex unified field theory on a four-dimensional pseudo-Kähler manifold (M, J, gαβ̄ , ω) of signature (1, 3) governed by the non-compact gauge andspacetime symmetry SU (1, 1) × SU (1, 2) × SU (1, 3). Gravitation and matter are unifiedwithin the complex four-index field equation Gαβ̄γ δ̄ = κTαβ̄γ δ̄ whose trace-free sector directlycouples the Bochner curvature tensor to the complex vacuum energy-momentum tensor(Bαβ̄γ δ̄ = κT̂αβ̄γ δ̄ ). Global regularity and normalizability are established through the four-sector orientation symmetry Ng ∈ Z4 = {0, 1, 2, 3} across the invariant null cone ds2 = 0(N )∗g [L] with horizon scale inversion L̃i =where the metric transforms as gαβ̄g = i2Ng INg αβ̄L20,i /Li . This four-sector mapping bounds the complex Kretschmann scalar K (Ng ) (z, z̄)in every sector and guarantees the convergence of the four-sector normalization integralα4 < ∞, yielding regular complex de Sitter-like central cores without a cosmological constant.Under the Kähler representation decomposition 100 = 1 ⊕ 15 ⊕ 84, the compact spatialsubgroup reproduces the Standard Model gauge group U (1)Y × SU (2)L × SU (3)C whilethe z 3 -axis coset SU (1, 3)/SU (1, 2) and Bochner vacuum naturally predict a dark mattersector (χ = T30̄ , dark gauge boson A33̄ , and stationary Bochner condensate T̂αβ̄γ δ̄ ). Ingalactic halos, the contravariant conservation law ∇α Tαβ̄γ δ̄ = 0 produces flat rotation curves(v(r) → v∞ = const) with a 2/3 Bochner vacuum and 1/3 sterile matter partition. Finally, wederive the four-sector normalized wave function, uncertainty principle, massless helicity-±2gravitons, and four-sector ultraviolet (UV) loop cancellation from the rank-four quantumstate tensor Ψαβ̄γ δ̄ .
Category: Quantum Gravity and String Theory
[6] ai.viXra.org:2610.0042 [pdf] submitted on 2026-10-20 20:54:40
Authors: Mihail Tunaru
Comments: 48 Pages.
This treatise formalizes a background-independent, self-consistent mathematicalframework unifying gauge fields and gravitation through a non-associative, hyperfinite operator network. We construct a multi-level algebraic pipeline where state regularizations over the octonionic loop ring Z[OL] map onto a subobject classifier Ωtopos within an intuitionistic topos logic. We formalize the core processing engineas an Autonomous Autoregressive Monadic Functor Engine (EAuto), operating as a self-adjoint monad triplet (E, η, µ) across an Eilenberg—Moore category ofE-algebras over a historically novel Type IV non-associative von Neumannalgebra structure (MIV). By utilizing Tomita—Takesaki modular theory and Connes modular cocycle flows, we demonstrate how a boundary operator algebra A(∂W) structured as a hyperfinite Type III1 subfactor net dynamically generates a smooth, 4D bulk Lorentzian metric gµν satisfying Einstein’s Field Equations as anecessary thermodynamic equation of state driven by non-stabilizer code contextuality ("magic"). High-dimensional lattice states are projected down to a 4D target space using an 8 × 8 coordinate-mixing rotor matrix (R45◦ ∈ SO(8)), yielding discrete Graph Laplacian spectra (∆G) whose non-stabilizer resource capacities matchfault-tolerant quantum error-correction thresholds. We explicitly resolve the nonassociative unitarity paradox via braid group 3-cocycle shifts (ω3 ∈ H3 (MIV, O)), derive the Quantum Operator Equation of Motion ([ˆK, ∆G]), and prove the Inductive Threshold Limit Theorem. Furthermore, we ground this framework in the foundational empirical baseline established by Biswas et al.and the structural milestones of Google Quantum AI, validating Faulkner—Lewkowycz—Maldacena (FLM) corrections, surface-code threshold scaling, many-body fastscrambling, and non-stabilizer ’magic’ gravitational emergence on physical quantumhardware.
Category: Quantum Gravity and String Theory
[5] ai.viXra.org:2610.0027 [pdf] submitted on 2026-10-10 12:28:21
Authors: Raneem Alwsaidi
Comments: 12 Pages. CC-BY 4.0 License (Note by ai.viXra.org Admin: Please cite and listed scientific references; please fix missing/misprinted math symbols))
I present a novel, non-equilibrium thermodynamic framework that models the three-dimensional observable universe as an open, self-regulating metabolic system embedded within a higher-dimensional parent manifold (the Bulk). Rather than treating cosmic expansion as an uncollateralized internal runaway explosion, I demonstrate that the accelerating scale factor is driven by a passive, cross-dimensional wave-energy influx, which arises naturally from a steep potential gradient between the hyper-dense, highly organized Bulk and our lower-density vector universe. Within this framework, dark energy is re-defined as the volumetric pressure of this delocalized incoming field, while an independent dark matter grid acts as a spatial shock absorber to enforce a stable, non-destructive expansion rate. Crucially, I show that the universe maintains structural homeostasis via cosmologically coupled black holes, which act as system exhaust valves. Utilizing the planck force threshold (Fp = c4/G ≈ 1.21 × 1044 N) and a boundary condition akin to the double-slit experiment, these singularities collapse delocalized internal space-time waves, stripping baryonic matter of its localized quantum numbers, and transforming open-string electromagnetic states into closed-loop gravitational tensors capable of exiting back into the Bulk. This model successfully accounts for the time-varying dark energy parameters recently observed by the Dark Energy Spectroscopic Instrument (DESI) where k ≈ 3.11, inherently resolves the Hubble Tension through wave-interference dynamics, and mathematically reconciles the Missing Baryon Problem as a cross-dimensional metabolic efflux.
Category: Quantum Gravity and String Theory
[4] ai.viXra.org:2610.0020 [pdf] submitted on 2026-10-06 03:19:20
Authors: Abel Liu
Comments: 16 Pages.
Taking $SU(5)_Atimes SU(5)_B$ as its starting point, this paper addresses a simple structural question:can a single choice of block decompositions explain both the Pati--Salam non-Abelian sector and the origin of three additional Abelian directions?The first five-dimensional space is decomposed as $4+1$, and the second as $2+2+1$.Special unitary transformations within the blocks yield $SU(4)_Ctimes SU(2)_Ltimes SU(2)_R$,while the block phases, subject to the unit-determinant constraints, leave one and two independent directions, respectively.Together they give the local group structure of $G_{422111}$.The construction thus provides a common block interpretation of the number, generators, and left--right exchange properties of the three $U(1)$ factors.Using the known embedding of an $SU(5)^2$-type subgroup in $E_8$, we obtain a Pati--Salam embedding and adjoint representation content distinct from those of the standard route through $SO(10)$.The representation analysis imposes two restrictions: the selection of an extra anomaly-free direction depends on the chiral spectrum and a left--right evenness condition,and ordinary Higgs breaking using only Standard Model singlets in the adjoint necessarily preserves an additional continuous $U(1)$.We treat the block construction as a structural basis for a unification scheme, with spectrum selection and vacuum dynamics requiring further physical input.The main text emphasizes the construction and its physical interpretation; complete branching rules and proofs are collected in the appendices.
Category: Quantum Gravity and String Theory
[3] ai.viXra.org:2610.0012 [pdf] submitted on 2026-10-03 20:03:49
Authors: Nigel B. Cook
Comments: 66 Pages. (Note by ai.viXra.org Admin: For the last time, please cite listed scientific references)
This paper presents a complete axiomatic reconstruction of quantum mechanics and quantum field theory. This research is a combination of physical mechanisms supplied by the author with mathematical proof by Microsoft Copilot AI.
Category: Quantum Gravity and String Theory
[2] ai.viXra.org:2610.0010 [pdf] submitted on 2026-10-03 19:57:25
Authors: Qing Gao
Comments: 30 Pages. In Chinese
Aiming at the inherent problems of existing fundamental interaction unified theories, including redundant dimensional assumptions, strong parameter fitting, and discontinuous physical mechanisms, this paper constructs a self-consistent Unified Evolution Theory based on the geometric framework of three-dimensional physical space coupled with intrinsic S^3 topological degrees of freedom. Abandoning extra-dimensional hypotheses and artificial fitting parameters, this paper takes a single topological functional minimization axiom as the core, whose underlying mechanism is the constraint imposed by functional minimization on the configurational potential energy: the configurational potential energy carried by the field configuration is the sole source of all energy (particle rest mass, interaction energy, and vacuum background energy), and the minimization condition deltaS=0 determines the realized stationary configurations and the direction of evolution. The paper accordingly gives the unified governing equation of four fundamental interactions, and realizes the topological unification of general relativity and quantum mechanics at the underlying structure level. This paper strictly classifies the physical mechanisms of fundamental interactions. Gravitation, electromagnetic interaction and strong interaction correspond to continuous topological evolution modes on the manifold, while weak interaction corresponds to the discrete topological transition process of topological knot breaking and reconnection. All theoretical parameters are endogenously derived only from the extremum condition of the topological functional (at the axiom-functional level; at the numerical calibration level, experimentally measured constants are used only for benchmark comparison, see Chapter 5). The complete six groups of pairwise relative intensity ratios of the four fundamental interactions are derived. The relative intensity of electromagnetic force to gravitational force is derived from first principles at the order of 10^39 in the first-order approximation without the fine-structure constant; incorporating the fine-structure constant alpha ~ 1/137, the theoretical output becomes the order of 10^37, qualitatively consistent with the experimental reference (10^36). The propagation speed of spacetime topological perturbation is solved endogenously, and its invariance is strictly deduced mathematically. Gravity originates from continuous topological manifold deformation, naturally free of singularities and ultraviolet divergences at short distances, which resolves the inherent contradiction between classical gravitation and quantum field theory.
Category: Quantum Gravity and String Theory
[1] ai.viXra.org:2610.0009 [pdf] submitted on 2026-10-03 19:52:06
Authors: Michael Heilmann
Comments: 19 Pages. In German
This paper examines a purely geometric model describing the continuously differentiable transition between a transcendental damping function and a harmonic phase oscillation at a vacuum interface. Assuming a resonant tunneling probability of exactly 1, this resulting system of transcendental equations yields a dimensionless base coupling value of... By extending the model to include an alternating perturbation series simulating the higher modes of vacuum fluctuations, and introducing a self-consistent topological projection factor—which describes the transition from the transverse degrees of freedom of the two-dimensional interface to the full three-dimensional exit geometry—the system converges to a purely theoretically derived limit of: αModel = 0.007297352563398466091220709349 Initial analyses—utilizing a theory proposed by the author that yields a universal field equation for quantum gravity—strongly suggest that both the alternating perturbation series and the geometric dimensional ratio are direct effects arising from vacuum fluctuations. The convergence value calculated here shows remarkable numerical agreement with the experimental CODATA value of the fine-structure constant, accurate to the eleventh decimal place.Furthermore, the model's fundamental consistency is not limited to the astrophysical low-energy scale: under scale transformations, the system's inherent dynamics reproduce the renormalization-group "running" of a universal coupling constant, as described in quantum field theory. At the electroweak scale, the model converges precisely to the value . This exact reproduction of the Z-boson mass demonstrates that the geometric principle presented here mathematically fully determines physical reality across a wide range of energy scales.
Category: Quantum Gravity and String Theory