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May 8, 2026Open Access

The Omnidimensional Quantum-Cosmological Theory — Version 2 — Mathematical Foundations Revised Rigorous Operator-Algebraic Reformulation with Worked Examples, Two-Loop Renormalization, and Falsifiability Audit

Key Points

To present a mathematically rigorous reformulation of the Omnidimensional Quantum-Cosmological Theory (OQCT), addressing previous assertions with strict proofs.
Revised the canonical commutator using a Lorentz-covariant constant tensor.
Derived the extended Born rule from the POVM-Gleason theorem.
Computed the renormalization-group beta function for the ethical coupling to two loops.
The extended Born rule is proven rather than postulated, reinforcing theoretical foundations.
The black-hole entropy's logarithmic correction is derived from the conformal anomaly, linking critical concepts.
Five practical examples are provided to illustrate theoretical applications and implications.

Abstract

This is a substantially revised and mathematically tightened reformulation of the Omnidimen-sional Quantum-Cosmological Theory (OQCT v1.0, April 2025). We retain the central1,3proposal — a 10-dimensional non-commutative operator manifold M10× C 6 × HQ withQC = Ran observer-coupling sector C 6 on which an SU(3) × U(1) gauge structure acts — but recastevery previous assertion under explicit hypotheses with rigorous proofs.What is new in v2 over v1.0: (i) the canonical commutator is rewritten with a Lorentz-covariant constant tensor θμν and the associative Moyal star product is proved to all orders informal deformation; (ii) the observer-coupling entropy functional SO is shown to be non-negative,jointly concave, and monotone under partial trace (quantum data-processing inequality analog);(iii) the extended Born rule is derived from a POVM-Gleason theorem, not postulated; (iv)the renormalization-group beta function for the ethical coupling is computed to two loops andthe fixed point is shown to be UV-attractive with explicit critical exponent; (v) the black-holelogarithmic correction αethic is derived from the conformal anomaly of the ethical gauge sector;(vi) the temporal triality operator is rigorously proved essentially self-adjoint with discretePlanck-unit spectrum; (vii) five worked examples are added (free particle, hydrogen with ethicalcorrection, two-slit, de Sitter, Schwarzschild); (viii) a transparent Status of the Theory tabledistinguishes proved theorems, stated conjectures, and phenomenological fits; (ix) the inflationprediction is explicitly framed as one phenomenologically consistent choice; (x) all unverifiedempirical citations from v1.0 have been removed. Keywords: non-commutative geometry; Moyal deformation; quantum gravity; operator man-ifold; observer-coupling sector; quantum entropy; POVM-Gleason theorem; renormalizationgroup; asymptotic safety; black-hole entropy; cosmological perturbations.MSC2020: 81T75; 83C45; 46L87; 81P15; 85A40.PACS: 04.60.–m; 04.62.+v; 11.10.Nx.

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