Gauge Structure from Admissible Non-Injective Projection (Q6a)

This repository contains the source of the Q6a Cosmochrony paper Gauge Structure from Admissible Non-Injective Projection.

Starting from the axiomatic foundation of admissible non-injective transitions (Foundation paper M), the paper derives the structure of gauge theory without introducing it as a postulate.

Results

• Gauge charges are identified as invariants of equivalence classes in the projection fibre: two configurations are gauge-equivalent when they project to the same observable state.
• The gauge group is the group of fibre-preserving transformations.
• (\mathrm{SU}(2)) is identified as the unique minimal non-abelian admissible group from the quaternionic structure of the admissible fibre; (\mathrm{U}(1)) arises as the residual phase symmetry; (\mathrm{SU}(3)) is a structurally motivated candidate extension whose derivation remains open.
• The gauge connection arises as the infinitesimal generator of fibre transport under varying projection, and Yang–Mills dynamics emerge from minimising the resulting curvature.

No dynamical substrate is required at any step; the derivations rest solely on Axioms A1–A4 of the Foundation paper and the spectral results of the O-series. Effective spacetime geometry, requiring the continuum limit of Q5a, is left to the companion papers of the emergent-geometry sub-programme.

Position in the programme

Q6a belongs to the gauge structure sub-programme (Presentation Note 3). Its inputs are the Foundation axioms (paper M), the quantum-structure results (Q1, Q2), and the spectral admissibility results (O12, O23, O27); the capacity bound it references is the capacity axiom [A-cap] of the companion capacity paper, with the Born–Infeld action as its saturation candidate.

Repository contents

q6a/
├── tex/          # LaTeX sources (Q6a.tex, bibliographies)
├── compile.sh    # pdflatex -> bibtex -> pdflatex x2, output in out/ (git-ignored)
└── README.md

Citation

J. Beau, Gauge Structure from Admissible Non-Injective Projection, Zenodo, 2026. DOI: 10.5281/zenodo.19655294

Links

• 🌐 Programme website: https://cosmochrony.org
• 💻 GitHub organization: https://github.com/Cosmochrony

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.