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[3] ai.viXra.org:2506.0135 [pdf] submitted on 2025-06-29 14:32:23
Authors: Yueshui Lin
Comments: 12 Pages.
This paper proposes a rigorous Third-order Enhanced Axiomatic System (TEAS) that resolves the fundamental conflict between quantum mechanics and general relativity within the framework of Woodin cardinals. By establishing an exact corre- spondence between renormalization group flow and categorical duality, we construct a quantum-classical fiber bundle mapping Q : H → Γ(T*M), derive the spacetime emergence mechanism k ~ log(ΛUV /ΛIR), and propose three fundamental axioms:quantum-classical correspondence, noncommutative geometric duality, and topological order stability.Key innovation: We establish the physical motivation for Woodin cardinals in quantum gravity through entropy scaling and renormalization completeness. The covering property of Woodin cardinals ensures the mathematical consistency of the quantum-to-classical transition, providing a set-theoretic resolution to Haag’s theorem. This approach differs from ∞-category methods by providing a set-theoretic foundation that resolves Haag’s theorem constraints through determinacy proper- ties.This work provides a mathematically consistent solution to the Haag theorem contradiction, offering a testable framework for quantum gravity theory with experimentally verifiable predictions.
Category: Mathematical Physics
[2] ai.viXra.org:2506.0034 [pdf] submitted on 2025-06-08 21:47:08
Authors: James McDaniel
Comments: 15 Pages. (Note by ai.viXra.org Admin: Author name is required in the article; please cite listed sceintific references)
This paper constructs the foundational structure of TOR (Topological and Recursive Motif Logic) as a definitional extension of the ZFC+++Qλ logical framework. TOR introduces a compression-resistant logic rooted in symbolic motif transitions, constructive witness chains, curvature metrics, and modal echo operators. Building upon ZFC, it formalizes motif behavior in terms of irreducibility, symbolic resonance, and recursive transitions across motif lattices. Appendices provide detailed examples, formal symbolic definitions, and semantic-witness interpretations, culminating in a logic capable of expressing both classical mathematical rigor and emergent symbolic structure. TOR is presented as a new foundational system for mathematics, cognition, and physical modeling.
Category: Mathematical Physics
[1] ai.viXra.org:2506.0008 [pdf] submitted on 2025-06-02 01:25:05
Authors: Rafael Eliahu Vaidergorn
Comments: 5 Pages.
This paper introduces the Vaidergorn Number (Ts), denoted by theHebrew letter Tzadi Sofit (Unicode U+05E5), as a novel mathemati-cal construct representing an absolute magnitude beyond all infinities. We formalize Ts within an extended Zermelo-Fraenkel (ZF) framework with new axioms, leveraging forcing and non-standard analysis, and prove its uniqueness via a new theorem, distinguishing it from Cantor’s cardinals (ℵ0, ℵ1) and Robinson’s hyperreals. Enhanced applications in cosmology model an infinite-yet-bounded universe with detailed derivations of a modified Friedmann equation and numericalsimulations, while string theory applications include a refined action with connections to braneworld scenarios. This preprint bridges mathematics and physics, inviting feedback and further exploration.
Category: Mathematical Physics