Published May 5, 2026 | Version 2
Preprint Open

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

Authors/Creators

Description

This is a substantially revised and mathematically tightened reformulation of the Omnidimen-
sional Quantum-Cosmological Theory (OQCT v1.0, April 2025). We retain the central
1,3
proposal — a 10-dimensional non-commutative operator manifold M10
× C 6 × HQ with
QC = R
an observer-coupling sector C 6 on which an SU(3) × U(1) gauge structure acts — but recast
every 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 in
formal 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 and
the fixed point is shown to be UV-attractive with explicit critical exponent; (v) the black-hole
logarithmic 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 discrete
Planck-unit spectrum; (vii) five worked examples are added (free particle, hydrogen with ethical
correction, two-slit, de Sitter, Schwarzschild); (viii) a transparent Status of the Theory table
distinguishes proved theorems, stated conjectures, and phenomenological fits; (ix) the inflation
prediction is explicitly framed as one phenomenologically consistent choice; (x) all unverified
empirical 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; renormalization
group; 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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Additional details

Software

Repository URL
https://github.com/cristiancmoises/oqct

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