Generative Structural Theory v1.108 — Depth-Six Probing at the Remaining Eighteen-Node Candidates
Year: 2026
Type: preprint
Abstract: This version establishes that each of twelve fixed eighteen-node candidate records, M1–M12, has an undecided stop with no feasible set and least detecting depth exactly six, with D = ∅ (no additional core deletion). The main search of v1.107 reported these twelve records as candidates with no feasible set that remained undetected at depth five. Version v1.107 established the result for M1; the remaining eleven were still search candidates. The present version checks the evidence for those eleven and brings all twelve fixed records to the same conclusion. For each record, four conditions are verified on the same input and stop: (P1) the forcing procedure ends undecided; (P2) no feasible set exists; (P3) depth-five probing does not decide “impossible”; and (P4) depth-six probing does. Together with monotonicity in the probing depth, these conditions establish least detecting depth exactly six. The infeasibility trees contain 15,553–66,375 nodes, the depth-five non-detection evidence contains 203–451 nodes, and the depth-six detection certificates contain 54–79 nodes. The distribution includes a verification appendix containing the fixed inputs, correspondence tables, evidence, trees, certificates, checkers, SHA-256 manifests, and instructions for rechecking all twelve records using Python and its standard library. Separate reference computations completed no comparisons within their time limits; no agreement with the reference implementation is claimed. The conclusion is restricted to these twelve fixed candidate records. It does not establish that depth six suffices for every eighteen-node case, that the records are pairwise non-isomorphic, or that (Q33) is settled. If a common detecting depth d as in (Q33) exists, the lower bound remains d ≥ 6.
Author: Okino, Koji
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225777022
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