Generative Structural Theory v1.16 — Fibre Structure Behind the Fixed-Census Separation

Abstract

GST v1.14 found, on a fixed single-arc census record, that the provenance-population condition Q_D selects a strictly smaller set of candidates than the recorded verdict condition E_rec. GST v1.15 characterised this difference conditionally through the fibres of a truncation map from full chain tuples to prefix chain tuples, leaving open which of two fibre types occurs on the fixed record. This version develops finite-product and end-point counting lemmas, together with a level recursion for counting chains without listing them. It applies a pre-registered counting method to recompute the relevant counts on the fixed inputs and compares the new results with the recorded values. In this computation, both candidates in the difference set have the injective fibre type B8-i: extensions exist and the full-chain tuple set is non-empty, but no prefix chain tuple has more than one full chain tuple above it. The recomputed counts agree with the record for all compared candidates and letters. Whether the truncation maps are also surjective on these candidates is not reported. The result concerns the fixed census and inputs; it is not a general classification theorem. The record premise PR, the eligibility of single-arc enlargements, and the identification of the implemented invariant with N4 remain unresolved. The computational checks are drafting-side checks, not independent verification. This release includes the paper in PDF and plain-text formats, a supplementary archive containing proofs, registrations, code, results and work records, and a SHA-256 distribution manifest. All files included in the supplementary archive are designated for public release.