Q1 — From Admissibility to Quantum Structure

This repository contains the source of the Q1 Cosmochrony paper From Admissibility to Quantum Structure: Phase Coherence and Correlations from Non-Injective Projection.

This paper establishes that quantum-mechanical phase coherence is not an independent postulate but a structural consequence of projective admissibility.

Core Result

The central theorem shows that any admissible transition preserves the Born–Infeld indiscernibility of conjugate Weil blocks $\rho_c$ and $\rho_{q-c}$ on the Heisenberg Cayley graph $\mathrm{Cay}(\mathrm{Heis}_3(\mathbb{Z}/q), S_q)$, and thereby maintains the metaplectic phase coherence of the admissible fibre. The proof rests on three independently established results: the minimal parity fibre structure of the non-injective projection (O18), the dynamical identity of conjugate Weil blocks (O17), and the discrete admissibility filter of projection locking (O22).

A constructive separating functional $R_n^{(c)}$ is exhibited and proved BI-admissible. Numerical validation for $q = 29$ across four conjugate pairs confirms $\operatorname{rank} W_n^{(c)} = 0$ exactly throughout the admissible regime — establishing structural indistinguishability of conjugate blocks as a representation-theoretic fact rather than a dynamical coincidence. The admissible fibre therefore carries complex amplitude structure with interference, the natural precursor of an effective Hilbert sector — without quantum mechanics as a postulate.

Keywords

Phase coherence, non-injective projection, Weil blocks, Born–Infeld indiscernibility, metaplectic phase, Heisenberg Cayley graph, emergent Hilbert space.

Repository Contents

q1/
├── code/        # Numerical validation scripts (+ requirements.txt)
├── tex/         # LaTeX sources (main + cosmochrony-bibliography.bib)
├── out/         # Compiled paper PDF (Q1-paper.pdf)
├── zenodo.json  # Zenodo deposition metadata
└── README.md

Links

• 🔗 DOI: 10.5281/zenodo.19561060
• 🌐 Website: https://cosmochrony.org/science/quantum-structure/q1/

Citation

J. Beau, From Admissibility to Quantum Structure: Phase Coherence and Correlations from Non-Injective Projection, Zenodo, 2026. DOI: 10.5281/zenodo.19561060.

Acknowledgements

Portions of the editorial refinement benefited from iterative interactions with large language models, used as analytical assistants. All claims and final formulations remain the sole responsibility of the author.