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

We establish a fibre-erasure theorem for the admissible coarse-graining hierarchy of the Cosmochrony spectral programme. The non-injective projection Π: Ω → O defines a residual fibre-information functional I(c;σ()), where c is a Weil-block fibre label and σc() is the BFS capacity profile at coarse-graining depth . The structural sufficiency hypothesis [H-suff] — that σ() is a sufficient statistic for the hierarchy beyond — is proved at the level of the BFS rank observable (Proposition prop:rank-suff), where the fibre label is erased identically; for the full Born–Infeld capacity it remains conditional on a single preservation step, numerically supported for q ∈ \61, 151, 211\ (Section sec:hsuff-test). Granting [H-suff], the data-processing inequality implies that I(c;σ()) is non-increasing in : fibre information is erased, not created, under admissible coarse-graining. This result is not a c-theorem; it does not count effective degrees of freedom. It is a quantitative realisation of the ENI no-go theorem: non-injectivity of Π forces projective information loss, and the data-processing inequality makes this loss monotone and measurable. The inter-sector variance Varc(σc()) serves as a computable proxy; its restriction to SU(3) colour-triplets connects directly to hypothesis [H-color].