Generative Structural Theory v1.12: A Complete P-TEXT Decision for a Certified Eight-Rank Instance — Witnessed Satisfiability, Certified Obstruction, and the Minimum-Cause Structure of a Single Conflict Cut
Year: 2026
Type: preprint
Abstract: This release presents Generative Structural Theory v1.12. For one fixed certified eight-rank instance, the paper gives a complete, UNKNOWN-free P-TEXT classification of all 7,616 provenance–rank cells. Of these cells, 7,548 are satisfiable and 68 are unsatisfiable. Every satisfiable verdict is supported by an exhibited partial-map witness accepted by a separately invoked checker. Every unsatisfiable verdict is supported by a forced-core certificate accepted by a separate verifier that replays the derivation and recomputes its recorded conditions. The 68 unsatisfiable cells occur at rank 9 and share two obstruction keys at the single conflict cut 3350. Exhaustive enumeration shows that the two keys have respectively four and six minimum-cardinality causes, each of cardinality two. Every minimum cause crosses the seed/cascade split, while the two cause supports and the two reply fans are disjoint. The paper also establishes that the forced maps are not monotone in rank in either containment direction. Across all 6,664 consecutive rank pairs, upward containment fails in 4,760 pairs and downward containment fails in 6,496 pairs. A post-stage-2 structural proposition localizes the obstructing provenances exactly: among the 952 provenances, obstruction occurs if and only if two specified chain-coordinate conditions hold. Their intersection contains 68 provenances; neither condition is sufficient by itself. This result is a coordinate localization, not a mechanism characterization. “Complete” refers only to the complete 7,616-cell population of this fixed certified instance. The release does not claim a complete decision procedure for P-TEXT in general, does not establish verdict monotonicity in rank, and does not answer the unbounded construction problem posed in v1.11. The deposit contains: the final manuscript; a reproducible evidence archive containing the v1.12 manuscript-stage materials and all three locked v1.12 evidence sets; and a self-excluding release manifest recording the archive and per-file SHA-256 values. The inherited instance and pinned verifier are not redistributed. Re-verification of those inherited primitives requires the separately published v1.10.1 and v1.11 materials identified in the paper.
Author: Okino, Koji
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213755539
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