Generative Structural Theory v1.10.1: Global Positional Selection — A Finite Extension Obstruction in a Certified n = 6 Cone Instance
Version v1.10.1 corrects four causal-attribution statements across three source locations in v1.10. The fatal rank-9 load is generated by the rank-9 seeds and forced propagation, not by routing through the pre-existing entries of the named rank-8 map. Theorem 7.2, its proof, certificates C1–C10, and the standalone theorem verifier are unchanged. Certificate C11, a seed-origin verification instrument, its negative control, and new claim-check controls have been added and independently verified. Generative Structural Theory v1.10.1 investigates the nested frozen-extension strategy proposed as a route toward the Positional-Map Theorem of GST v1.9. That strategy attempts to construct a global positional selection rank by rank, extending each policy-consistent partial selection without revising any previously decided entry. This paper proves that the corresponding Finite Extension Lemma fails at a named instance. In the certified n = 6 cone identified by the bundled instance digest, a policy-consistent rank-8 partial selection closes through rank 8 but admits no frozen policy-consistent extension closing through rank 9 under final-demand semantics. The obstruction occurs at a single newly reached key. The unique simulation-class-maximising reply forces a second assignment, whose fixed-point propagation enlarges the load at an already-frozen cut and leaves its obligation with no sufficient reply. The proof is finite and deterministic and does not depend on the exploratory search that found the obstruction. The release includes the corrected paper, a standalone verification package, certificates, provenance reconstruction, mutation controls, manifests, clean-room reproducibility gates, a correction record, and source and rendered-text diffs from v1.10. The result refutes the proposed finite-extension route at the certified instance; it does not refute the Positional-Map Theorem, does not prove unbounded simulation rank, and makes no claim for general n or ranks beyond 9.
Authors
- Koji Okino (ORCID: https://orcid.org/0009-0003-9273-9813)
Institutions
- United States Department of Labor (US)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-09-19
- DOI
- https://doi.org/10.5281/zenodo.22717258
- Primary Topic
- Philosophy and History of Science
- Type
- preprint