Generative Structural Theory v1.18 — Reconstructed End Points and Certified Residual Filtering for Two Fixed-Census Arcs

Abstract

GST v1.16 isolated a fixed-census separation and two candidate arcs, and GST v1.17 recorded a single end point and a unique extension for each of their extended letters, without identifying these cuts or explaining their uniqueness. This version identifies the end points and extensions for arcs 4 and 24, for letters 0, 2 and 3, through a pre-registered, locked reconstruction (route C). It then establishes acceptance or exclusion under the residual conditions for six registered targets per arc using generated and verified certificates. Exclusion certificates record finite derivations with strictly decreasing rounds; acceptance certificates provide finite closed relations. For letter 2, the end point is excluded by exactly 12 residuals in arc 4 and 11 in arc 24, while adding the pair 4>1 yields a candidate accepted by every residual. Two candidate cuts examined at the last prefix pair for letter 0 each violate a residual condition. Together with candidate lemmas derived from the definitions, the certified results establish the existence and form of the extension from each specified end point. The claims are explicitly separated by their evidence. The chain reaching an end point and the uniqueness of that end point remain conditional on the reconstruction's written universes and predecessor relations, which the certificates do not verify as a whole. A common structural explanation for the residual exclusions and acceptances remains open; generality beyond the two arcs is not claimed. Certificate generation and verification were performed by the drafting side, using shared fixed definitions, rather than an independent implementation. The supplementary archive contains registrations, LOCK and permission records, source code, controls, run outputs, certificates, SHA-256 manifests, and instructions for restoration and re-verification, including the original-path requirement.