Overview
This article establishes a fibre-erasure theorem for the admissible coarse-graining hierarchy of the Cosmochrony spectral programme. 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 a structural sufficiency hypothesis [H-suff], the data-processing inequality implies that this functional is non-increasing in \(\ell\): fibre information is erased, not created, under admissible coarse-graining.
The result is a quantitative realisation of the ENI no-go theorem. Non-injectivity of \(\Pi\) forces projective information loss, and the data-processing inequality makes this loss monotone and measurable along the BFS resolution axis. 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 the [H-color] campaign of the O-series.
Core contributions
- Monotone information functional. A residual fibre-information functional \(I(c;\sigma(\ell))\) is defined for the BFS coarse-graining hierarchy and shown, conditional on [H-suff] and [H-sg], to be non-increasing in \(\ell\) (Theorem 4.1).
- Rank-level unconditional result. At the BFS rank observable, the fibre label is erased identically by Schur's lemma (Proposition 3.6). The semigroup property [H-sg] is moreover redundant at this level (Corollary 3.7).
- Capacity-level numerical evidence. Permutation-based Spearman tests on BFS capacity data for \(q \in \{61, 151, 211\}\) detect no significant fibre-label dependence in step-by-step residuals, providing direct numerical support for [H-suff].
- Fibre-erasure equilibrium. The condition \(I(c;\sigma(\ell)) = 0\) identifies a fixed-point profile \(\sigma^*\) approached in the thermodynamic limit \(q \to \infty\) with \(\mathrm{O}(q^{-1/2})\) corrections.
- Three-axis disambiguation. The coarse-graining axis \(\ell\), the thermodynamic axis \(q \to \infty\), and the temporal cascade axis \(n\) (PTO) are structurally orthogonal and each carry their own information functional.
Strict disclaimer
This result is not a \(c\)-theorem. It does not count effective degrees of freedom. It is a quantitative information-loss statement attached to the Weil-fibre label under coarse-graining. A \(c\)-theorem-type statement would require an additional counting principle for effective degrees of freedom, which is not established here and is listed as open problem [O-2].
What the theorem does and does not establish
Establishes, conditional on [H-suff] and [H-sg]: a monotone information functional for the BFS coarse-graining hierarchy; its non-increase under depth-increment; the identification of \(I(c;\sigma(\ell)) = 0\) as the fibre-erasure equilibrium.
Does not establish: a \(c\)-theorem; 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]).
Relation to the Cosmochrony programme
Fibre Erasure occupies a hub position in the programme. It takes as input the ENI no-go theorem (which establishes \(S_\Pi > 0\) but does not order information loss across resolutions) and the spectral admissibility programme (which provides the operational hierarchy \(\sigma_c(\ell)\)), and connects them by translating the ENI projection entropy into the operational information functional \(I(c;\sigma(\ell))\). Together with the PTO paper, which handles the orthogonal temporal axis \(n\), it constitutes the information-theoretic architecture of the admissibility cascade.
References
Jérôme Beau. Projective Information Loss and Fibre Erasure in Admissible Non-Injective Projection. Working paper, Zenodo. 10.5281/zenodo.20466459