Generative Structural Theory v1.19 — The K1c Roots of the GST v1.18 Certificates: What the Records Show, and a Conditional Procedural Account of the Stored Answer

This study examines the recorded root answers in two GST v1.18 certificate files. At three distinct residuals, comprising four arc–residual pairs classified as K1c, the recorded answer is y = z_t − {1>3}, rather than z_t. It separates two questions: whether (X′, z_t) belongs to the recorded acceptance relation, and which procedure fixed the stored answer.A registered reading finds both (X′, y) and (X′, z_t) in the recorded relation at all four target pairs. The relation’s closedness rests on the earlier verification record, subject to the stated provenance limitations. A comparison of the fixed certificate and targets files also confirms agreement of the target value adopted by the evaluator’s and extractor’s rules.Static examination of specified code versions shows that the generator stores the candidate of least cut value, the verifier checks the stored answer without selecting it, and the extractor transcribes it. This yields a conditional procedural account: if the generator version examined wrote the stored answers, y was its least candidate. It does not establish mathematical uniqueness.The contemporaneous records examined do not fully establish which code versions the past runs executed. The actual generator candidate sets remain unknown, and applications of the cited lemmas retain the stated cone-membership condition. The structural questions associated with the v1.18 open item O1 remain unresolved.The supplementary archive contains the cited working records, including corrections and addenda, with a records table and SHA-256 manifest. Their inclusion does not constitute independent verification of their contents.