Research · Papers · Formal verification and machine-checked proof · ML-030
On the soundness of the verifier-level Phase-Trellis P5 model
Within the verifier-level Phase-Trellis P5 model class, checker replays confirm Court Zero legality, and the fixed ITER19 K0 relation admits an exact adapter.
Published 2026-08-29
For everyone
Plain summary
ML-030 tracks an open route toward conditional target 18,801 using a verifier-level Phase-Trellis P5 model. A phase-trellis carries phase rules from one column to the next. The checker confirms Court Zero legality and verifies an exact adapter for the relation ITER19 K0. These checks confirm structure and replayability, but not soundness: accepted runs can still be invalid. The natural-hull sample fails soundness, and the ITER19 K0 adapter fails on all eight real SHA round-0 cases for the lowest three bits. The register contains no K1 candidate and no verifier-shaped 32-column p5 candidate. General alternative trellises remain untested. The entry status is CONJECTURE, with no corrections or prior-art records in the register.
Result
Within the verifier-level Phase-Trellis P5 model class, checker replays confirm Court Zero legality, and the fixed ITER19 K0 relation admits an exact adapter. However, the natural-hull sample fails soundness, and the ITER19 K0 adapter fails soundness on all eight real SHA round-0 low-three-bit cases.
The register records no K1 candidate and no verifier-shaped 32-column p5 candidate. General alternative trellises remain untested. With the conditional target at 18,801 unreached, the status remains CONJECTURE.
Setting and definitions
The register labels this phase-trellis model P5, with named relation variants K0 and K1. ITER19 K0 denotes the fixed relation audited under adapter replay. The natural-hull sample is the supplied baseline sample constructed from the natural hull. An exact adapter is the verified conversion module checked by the replay suite.
Court Zero is the verifier's legality condition on globally allocated cyclic paths. Soundness requires that every state accepted by the relation is valid under the target specification. The model class distinguishes verifier-shaped 32-column p5 candidates from general alternative trellises. The count 18,801 is a conditional target rather than an achieved result.
Method
Verification paired a verifier-legality audit with exhaustive adapter replay across all 131,072 one-column assignments and eight real SHA round-0 low-three-bit cases.
The legality audit verified Court Zero compliance for the P5 class, and the replay confirmed an exact adapter for ITER19 K0. Soundness evaluation showed failure on the natural-hull sample and failure across all eight SHA round-0 test cases for the adapter.
Audit and replay receipt records are provided in this paper's downloadable evidence pack.
Discussion
Legality and exact adapter conversion do not imply soundness. The audit establishes that the Phase-Trellis P5 model class obeys Court Zero path rules and that ITER19 K0 converts under the adapter, but the soundness counterexamples on the natural-hull sample and all eight SHA round-0 low-three-bit cases leave the route open.
The absence of a K1 candidate or a verifier-shaped 32-column p5 candidate narrows the validated search space, while untested alternative trellises leave the broader class unresolved. Target 18,801 remains a route condition rather than an attained metric. Curation notes list corrections as NONE, with no corrections trail entry and no prior-art position recorded.
For everyone — the takeaway
What this means
The proposed P5 phase-trellis follows the verifier's structure rules, and its fixed ITER19 K0 case converts cleanly through the adapter. But both the baseline sample and that conversion fail soundness: they accept invalid states on all eight real SHA round-0 test cases. Because other phase trellises remain untested, the route stays open and the entry remains a CONJECTURE toward target 18,801.
Register references
- Entry: ML-030.
- Receipt artifacts:
phase_trellis_p5_verifier_legality_audit.json,ghost_iter19_k0_phase_trellis_adapter_receipt.json. - Prior-art work: the register does not record this.
Every artifact named above is bundled in, or hashed by, this paper's evidence pack below.
Evidence pack
Everything needed to check this entry against its receipts: the register text, a manifest with a SHA-256 hash for every named receipt, and 0 of 0 receipt files bundled (1 KB). Anything not bundled is still hashed in the manifest and lives in the compute-box working trees.
Changelog
Last reviewed 2026-08-29
- 2026-08-29Published on this site.