Projective Information Loss and Fibre Erasure in Admissible Non-Injective Projection

This repository contains the source of the Fibre Erasure Cosmochrony paper Projective Information Loss and Fibre Erasure in Admissible Non-Injective Projection.

This work establishes a fibre-erasure theorem for the admissible coarse-graining hierarchy of the Cosmochrony spectral programme.

Quick Summary

The non-injective projection $\Pi : \Omega \to \mathcal{O}$ defines a residual fibre-information functional $I(c;\sigma(\ell))$, where $c$ is a Weil-block fibre label and $\sigma_c(\ell)$ is the BFS capacity profile at coarse-graining depth $\ell$.

Conditional on the structural sufficiency hypothesis [H-suff], the data-processing inequality implies that $I(c;\sigma(\ell))$ is non-increasing in $\ell$:

Fibre information is erased, not created, under admissible coarse-graining.

[H-suff] is proved at the level of the BFS rank observable (Proposition 3.6, label-blindness from Schur's lemma) and numerically supported at the full Born--Infeld capacity level for $q \in {61, 151, 211}$.

Core Result

The fibre-erasure theorem (Theorem 4.1) states: under [H-suff] and [H-sg] (semigroup property, redundant at the rank level), for any $\ell' > \ell$, $$ I(c;\sigma(\ell')) \le I(c;\sigma(\ell)). $$

The inter-sector variance $\mathrm{Var}_c(\sigma_c(\ell))$ serves as a computable proxy. Its restriction to $\mathrm{SU}(3)$ colour-triplets connects directly to hypothesis [H-color] of the O31--O32 campaign.

Conceptual Structure

This paper connects the qualitative ENI no-go theorem with the quantitative spectral convergence observed numerically across $q \in {61, 151, 211, 307}$:

• ENI establishes $S_\Pi > 0$ but does not order information loss across resolutions.
• Fibre Erasure introduces the coarse-graining axis $\ell$ and turns ENI into a monotone, measurable hierarchy via the data-processing inequality.

Three orthogonal axes are disambiguated:

Axis	Parameter	Role
Coarse-graining / resolution	$\ell$ (BFS depth)	this paper, carries $I(c;\sigma(\ell))$
Thermodynamic / continuum	$q \to \infty$	limit for the universal profile $\sigma^*$
Temporal / cascade	$n$ (cascade step)	projective time, handled by PTO

Strict Disclaimer

This result is not a $c$-theorem. It does not count effective degrees of freedom. A $c$-theorem-type statement would require an additional counting principle, listed as open problem [O-2].

What This Paper Establishes

Conditional on [H-suff] and [H-sg]:

• a monotone information functional $I(c;\sigma(\ell))$ for the BFS coarse-graining hierarchy;
• its non-increase under depth-increment, via the data-processing inequality;
• the identification of $I(c;\sigma(\ell)) = 0$ as the fibre-erasure equilibrium condition (Corollary 4.4).

What This Paper Does Not Establish

• a $c$-theorem or analogue (open problem [O-2]);
• the full capacity-level form of [H-suff] (proved at the rank level; pointwise Born--Infeld residue open as [O-1a$'$]);
• the full capacity-level form of [H-sg] (proved at the rank level and there redundant; capacity-level residue open as [O-1b]).

Position in the Programme

Fibre Erasure occupies a hub position between the foundational papers and the spectral admissibility programme:

• inputs: ENI (non-injective projection, projection entropy $S_\Pi$) and Foundation (Weil-fibre realisation);
• inputs: spectral programme (BFS capacity profiles $\sigma_c(\ell)$, numerical campaigns, [H-color] hypothesis);
• output: information-theoretic monotone connecting them.

Together with the PTO paper (which handles the orthogonal temporal axis $n$), it constitutes the information-theoretic architecture of the admissibility cascade.

Build

bash compile.sh

Output: out/FibreErasure.pdf.

Keywords

Non-injective projection; fibre erasure; admissible coarse-graining; data-processing inequality; information monotone; BFS capacity; spectral admissibility; projective information loss; Weil representation; Heisenberg group; [H-color].

Citation

If you reference this work, please cite:

J. Beau, Projective Information Loss and Fibre Erasure in Admissible Non-Injective Projection, Zenodo, 2026.

Acknowledgements

Portions of the formal development, numerical validation, and editorial refinement benefited from iterative interactions with large language models, used as analytical assistants for testing internal consistency and exploring alternative formulations. All theoretical results and interpretations remain the sole responsibility of the author.

Contributions

This repository is intended as a research reference. Critical feedback, mathematical scrutiny, and independent analyses are welcome. Please open an issue to discuss conceptual points or technical details.