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: O defines a residual fibre-information functional I (c; () ), where c is a Weil-block fibre label and c () is the BFS capacity profile at coarse-graining depth. The structural sufficiency hypothesis H-suff — that () 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; () ) 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 forces projective information loss, and the data-processing inequality makes this loss monotone and measurable. The inter-sector variance Varc (c () ) serves as a computable proxy; its restriction to SU (3) colour-triplets connects directly to hypothesis H-color.