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| viXra.org > High Energy Particle Physics > 2605 |
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[2] viXra:2605.0030 [pdf] submitted on 2026-05-09 22:27:05
Authors: Fabrizio Vassallo
Comments: 38 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We propose a discrete geometric model in which classical spacetime and matter emerge from a discrete random network equipped with two combinatorial structures: Ollivier-Ricci curvature (ORC), a metric-free notion of curvature defined via optimal transport on the network, and discrete Cartan torsion, a 2-cochain on a weighted simplicial complex measuring holonomy defects of parallel transport around elementary triangles. Both structures are intrinsically combinatorial and require no background geometry; classical geometry is an output, not an input, of the model. Building on Trugenberger's ORC-based network model, which exhibits a phase transition between a random hyperbolic phase and a geometric phase, we augment the Ricci flow with a nonlinear torsion coupling and demonstrate, in an explicit four-node toy model, that the resulting dynamical system possesses two distinct basins of attraction whose separation is topologically robust and independent of the specific toy model chosen. Regions of the network with vanishing torsion condense into a one-dimensional geometric phase (embryonic spacetime), while regions with non-vanishing torsion condense into a localized, topologically non-trivial configuration identified as a torsion defect carrying all quantum numbers equal to zero. A key structural result is that the torsion-bearing fixed point P T is a saddle point of the linearized discrete flow, with one expanding and one contracting direction in the (w, T) plane. The Jacobian entry J T w = 8λ/9 > 0 is derived exactly from the Wasserstein optimal transport, yielding real eigenvalues µ = 1 ± 8λη sech 2 (T *)/9 and a determinant det(J) = 1 − (8λη/9) sech 2 (T *) < 1. We conjecture-as a structural analogy motivated by the geometry of Einstein-Cartan theory, but not derivable from the linearized dynamics-that this fixed point is geometrically associated with the parametrization of the Cartan helix. This conjecture motivates, but does not rigorously imply, the hierarchical level model introduced in Section 7, in which the rotation angle and expansion factor of the helix are tentatively associated with spin halving and mass scaling between levels. We further propose a hierarchical particle spectrum-the level model-in which each level is characterized by doubled spacetime dimension, halved spin, and mass scaling by a factor 4α, where α is the 1 electromagnetic fine-structure constant and δ F ≈ 4.6692 is the Feigenbaum period-doubling constant. The conservative flow has a saddle-like structure at P T and cannot produce a Feigenbaum period-doubling cascade. We introduce a physically motivated dissipative extension of the torsion equation-a −ξ sin(T) restoring term-and show that the resulting effective torsion dynamics reduces, in the strongly dissipative limit, to the sine mapT → ξ sin(T) on [0, π], which belongs to the Feigenbaum universality class. The Feigenbaum constant δ F ≈ 4.6692 therefore emerges dynamically from the flow, and the empirical relation α ≈ 1/(2πδ 2 F) is found to be numerically consistent with this scaling, with the factor 2/π from the sine map amplitude. The physical origin of the dissipation is the geometric coarse-graining at each RG step: information is globally conserved, but the geometric distinguishabil-ity of sub-Planckian torsion configurations is reduced, creating equivalence classes in the sense of 't Hooft's dissipative quantum gravity program [82]. Our results and 't Hooft's program converge toward the same conceptual conclusion by independent routes: quantum-mechanical behavior can emerge from an effectively dissipative underlying structure, with information globally conserved. The continuum limit of the full construction is argued to reproduce Einstein-Cartan gravity in four dimensions. Falsifiable numerical predictions are formulated for simulation on synthetic networks.
Category: High Energy Particle Physics
[1] viXra:2605.0023 [pdf] submitted on 2026-05-08 10:45:55
Authors: Davor Palle
Comments: 8 Pages.
The production of the longitudinally polarized same-sign W boson pairs at the LHCpp collisions presents the unique opportunity to study and verify in detail the mechanism ofthe symmetry breaking in the Standard Model and beyond.We compare at leading order the electroweak contribution to this productionin the Standard Model and in the theory of the noncontractible space containing the zero-normmassless zeta particle. It appears that the difference between differential cross sectionsis huge with the possibility to measure it in Run 3 and high-luminosity runs of the LHC.
Category: High Energy Particle Physics
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