OQCT — Omnidimensional Quantum-Cosmological Theory

Version 2 — Mathematical Foundations Revised A rigorous operator-algebraic framework unifying quantum field theory, general relativity, and observer-coupling physics through a 10-dimensional non-commutative manifold.

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📄 Latest Paper

📥 Download OQCT v2 (PDF) — 21 pages · May 2026 📥 LaTeX source 📥 v1 archive — superseded April 2025 version

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🌌 Overview

OQCT proposes a 10-dimensional non-commutative operator manifold

\mathcal{M}^{10}_{\mathrm{QC}} = \mathbb{R}^{1,3} \times \mathcal{C}^6 \times \mathcal{H}_{\mathrm{Q}}

where \mathbb{R}^{1,3} is Minkowski spacetime, \mathcal{C}^6 is an observer-coupling fiber with \mathrm{SU}(3)\times\mathrm{U}(1) gauge structure, and \mathcal{H}_{\mathrm{Q}} is the quantum Hilbert space.

The theory addresses three crises of modern physics within a single variational principle: the quantum–gravity divide, the measurement problem, and the role of the observer.

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✨ What is new in Version 2

Version 2 is a complete mathematical reformulation of the April 2025 v1 preprint. Every previous claim has been re-examined and either proved as a theorem, demoted to a falsifiable conjecture, or labeled as phenomenological.

Change	v1 (April 2025)	v2 (May 2026)
Canonical commutator	[\hat x^\mu,\hat x^\nu]=i\ell_P^2\varepsilon^{\mu\nu\rho}\hat x_\rho ❌ not Lorentz-covariant	[\hat x^\mu,\hat x^\nu]=i\theta^{\mu\nu}\hat{\mathbf{1}} ✓ Seiberg–Witten form
Moyal associativity	Claimed	Proved to all orders
Entropy properties	Asserted	Non-negativity, joint concavity, DPI all proved
Extended Born rule	Postulated	Derived from POVM-Gleason theorem
Collapse criterion	Theorem-claim	Falsifiable conjecture
Beta function	One-loop	Two-loop with UV-attractive fixed point proved
BH log correction	Asserted	Derived from conformal anomaly
Triality operator	Malformed bra-ket	Clean direct sum, self-adjointness proved
Inflation n_s = 0.9649	"Derivation"	Phenomenological consistency (any Starobinsky model fits)
Fictitious citations	Stanford Neuroquantics Lab	Removed
Author epigraph	Mystical quote	Removed (improper register)

See CHANGELOG.md for the full revision history.

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📐 The Master Equation

|\Psi\rangle = \int_{\mathcal{M}^{10}_{\mathrm{QC}}}\left[i\hbar\partial_t\Psi + \sum_k \hat{a}^\dagger_k\hat{a}_k\otimes\hat{g}_{\mu\nu} + \gamma^\mu D^{\mathrm{obs}}_\mu\psi_{\mathcal{O}} + \lambda_\Omega\,\Phi(\Omega)\right]\sqrt{-G}\,\hat{d}^{10}x = 0

Term	Physical meaning
i\hbar\partial_t\Psi	Quantum temporal evolution (Schrödinger)
\hat{a}^\dagger_k\hat{a}_k\otimes\hat{g}_{\mu\nu}	Particle–spacetime entanglement
\gamma^\mu D^{\mathrm{obs}}_\mu\psi_{\mathcal{O}}	Covariant observer-coupling propagation
\lambda_\Omega\Phi(\Omega)	Multiplicity entropy modulation

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🔬 Status of Results in v2

✅ Proven Theorems

• NC algebra Jacobi identity
• Moyal star associativity (all orders)
• Master equation gauge invariance
• Hermiticity / unitarity of time evolution
• Probability current conservation
• Classical limits to GR, QFT, Dirac, Schrödinger
• S_{\mathcal{O}} non-negativity, joint concavity, partial-trace monotonicity
• Extended Born rule from POVM-Gleason
• Two-loop \beta_\lambda with UV-attractive fixed point
• Black-hole logarithmic correction \alpha_{\mathrm{ethic}}\approx-1.52
• Temporal triality operator self-adjoint with discrete Planck spectrum

⚠️ Falsifiable Conjectures

• Ethical-gradient collapse criterion
• Page-curve restoration during Hawking evaporation

○ Phenomenological Fits

• Conscious inflation prediction n_s\approx 0.965 (consistent with Planck 2018, but not unique to OQCT)

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🧪 Experimental Predictions

#	Signature	Falsified if...
E1	CMB B-mode TB cross-correlation at \ell\sim 3000, amplitude \sim 10^{-3}	CMB-S4 measures null at this precision
E2	Microtubule decoherence time \sim 25 ms at 310 K	Ultrafast spectroscopy measures \ll 1 ms
E3	Visibility deviation in $\hat{\mathcal{E}}$-biased interferometry	No deviation detected at predicted amplitude
E4	BH log correction \alpha\approx-1.52 (vs. LQG: -1/2, string: -3/2)	Competing computation matches Hawking spectrum better
E5	UV-attractive fixed point in graviton scattering	Higher-loop or non-perturbative result kills it

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📁 Repository Structure

oqct/
├── index.html                              # Interactive website (v2 updated)
├── README.md                               # This file
├── CHANGELOG.md                            # Full v1 → v2 change log
├── CITATION.cff                            # Citation metadata
├── LICENSE                                 # CC BY 4.0
├── images/
│   └── screen.png                          # Website preview screenshot
└── paper/
    ├── OQCT_v2_Moises_2026.pdf             # Current paper (21 pages)
    ├── OQCT_v2_Moises_2026.tex             # LaTeX source
    ├── OQCT_v1_Moises_2025.pdf             # Archived v1 (superseded)
    └── OQCT_v1_Moises_2025.tex             # Archived v1 source

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🌐 Live Website

The index.html is deployed via GitHub Pages at:

https://cristiancmoises.github.io/oqct

Five sections rendered with MathJax 3:

• Theory — abstract, master equation, status of the theory
• Mathematics — theorem-proof boxes, Moyal product, entropy bounds, RG flow, BH entropy
• Experiment — interactive spacetime canvas + falsifiable predictions
• Overview — plain-language analogies for non-specialists
• References — bibliography with DOI links

Enable GitHub Pages

1. Repository Settings → Pages
2. Source: Deploy from a branch → main / root
3. Save — site goes live at the URL above

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📖 Citation

@misc{moises2026oqct_v2,
  author       = {Mois\'{e}s, Cristian Cezar},
  title        = {{The Omnidimensional Quantum-Cosmological Theory (OQCT) ---
                   Version 2: Mathematical Foundations Revised}},
  year         = {2026},
  month        = may,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.XXXXXXX},
  url          = {https://github.com/cristiancmoises/oqct},
  note         = {Preprint v2 supersedes v1.0 (April 2025).
                  MSC2020: 83C45, 81T75, 46L87, 85A40, 81P15}
}

Replace XXXXXXX with your Zenodo DOI once published.

A machine-readable CITATION.cff is also provided.

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📚 Key References

The full bibliography is in the paper. Selected works:

• Connes, A. Noncommutative Geometry. Academic Press (1994).
• Seiberg, N. & Witten, E. JHEP 09 (1999) 032.
• Busch, P. Phys. Rev. Lett. 91 (2003) 120403. DOI:10.1103/PhysRevLett.91.120403
• Lieb, E. H. Adv. Math. 11 (1973) 267–288.
• Lindblad, G. Commun. Math. Phys. 48 (1976) 119–130. DOI:10.1007/BF01608499
• Gibbons, G. W. & Hawking, S. W. Phys. Rev. D 15 (1977) 2752. DOI:10.1103/PhysRevD.15.2752
• Page, D. N. Phys. Rev. Lett. 71 (1993) 3743–3746. DOI:10.1103/PhysRevLett.71.3743
• Planck Collaboration. Astron. Astrophys. 641 (2020) A6. DOI:10.1051/0004-6361/201833910
• Reuter, M. Phys. Rev. D 57 (1998) 971–985. DOI:10.1103/PhysRevD.57.971

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🤝 Contributing

This is an independent research project. Comments, corrections, and substantive criticism are very welcome.

• Open an issue for mathematical errors, typos, or proposed clarifications
• Pull requests for the website (index.html) or LaTeX (paper/)
• Discussion of physics interpretation: open a Discussion thread

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👤 Author

Cristian Cezar Moisés Independent Researcher · Caxias do Sul, RS, Brazil ✉️ ccm@riseup.net 🐙 github.com/cristiancmoises

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📜 License

This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

You are free to share and adapt for any purpose, provided appropriate credit is given.

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⚠️ Honest Status

OQCT is an independent theoretical proposal, not a peer-reviewed established theory. Version 2 represents a substantial improvement in mathematical rigor over version 1, but several core conjectures remain open. Readers should evaluate the work on the merit of its proofs, not on the boldness of its claims. Falsification criteria are explicitly stated for every conjecture.