Research · Papers · The quadratic hull and its defects · ML-022
Unsoundness of the fixed Ghost-P5 ITER19 allocation and K0 trellis adapter
Ghost-P5 (18,801, ITER19): deg-2 hull spans 17-bit space, δvert=66, δflip=2; exact K0 adapter unsound on all 131,072 replayed assignments
Published 2026-08-29
For everyone
Plain summary
ML-022 tests a specific setup for Ghost-P5, a proposed route for encoding large computations. An allocation specifies the fixed set of intermediate values kept during the run. The test found that the fixed ITER19 allocation eliminates none of the 17-bit search space when restricted to equations spanning at most two variables; this surviving space is its degree-2 hull. The census tallied 7,245 valid assignments against 123,827 invalid ones. An exhaustive check of all 131,072 one-column assignments through the fixed K0 trellis adapter accepted incorrect data on all eight concrete test inputs listed in the register. This fixed design is parked. Alternative allocations and rule presentations remain open. The register records no prior-art position.
Result
For the Ghost-P5 existential route targeting 18,801, the fixed ITER19 allocation produces a degree-2 hull spanning the entire 17-bit ambient space, with defect values δvert=66 and δflip=2. The exact K0 trellis adapter is unsound across all 131,072 replayed one-column assignments on all eight concrete SHA round-0 low-three-bit inputs. The stationary delta-4 and delta-20 translation covers are dead.
The fixed full-relation presentation and the fixed ITER19 trellis checkpoint are barred from resumption. Alternative allocations, K1 relations, transient covers, lifts, and selector-chosen existential subrelations remain UNKNOWN. The entry holds LIVE-PARKED status.
Setting and definitions
Ghost-P5 existential is the ML-022 route targeting 18,801. ITER19 denotes the fixed allocation exported in the entry. K0 is the adapter's fixed trellis relation; K1 is an unresolved alternative family. A fibre is one of 4,096 contexts in the census. The degree-2 hull comprises all 17-bit assignments satisfying every degree-at-most-2 relation. δvert and δflip record defect metrics without internal expansions.
A one-column assignment fixes the values in a single trellis column. Soundness requires that the adapter accept only assignments satisfying the target relation. A stationary translation cover applies an identical translated cover family across all active positions; delta-4 and delta-20 name the two evaluated families.
Method
The fixed ITER19 allocation was evaluated across 4,096 fibres following earlier 56/72-context kills. The census separated 7,245 honest assignments from 123,827 non-conforming assignments, deriving the degree-2 hull and both defect values.
The K0 trellis adapter underwent exhaustive replay over all 131,072 one-column assignments, failing soundness on all eight concrete SHA round-0 low-three-bit inputs. The delta-4 and delta-20 stationary translation covers were tested and ruled dead.
Discussion
These checks eliminate the ITER19 allocation, the K0 adapter, and the two stationary translation-cover families. The ledger bars both the full-relation presentation and the ITER19 checkpoint from future runs.
The broader Ghost-P5 route remains open. K1 relations, transient covers, lifts, and selector-chosen existential subrelations remain UNKNOWN. The eight SHA counterexamples establish unsoundness strictly for the tested K0 adapter configuration. The register records no prior-art position.
For everyone — the takeaway
What this means
The current Ghost-P5 setup cannot enforce soundness. Its degree-2 checks leave all 17 bits unconstrained, and the column adapter accepts invalid data on every tested input. This specific ITER19 allocation and K0 adapter are abandoned. The overall Ghost-P5 question stays open because alternative allocations, lifts, and relation formulations have not been tested. The register records no prior-art position.
Register references
ML-022. Receipt artifacts: CONT ghost_p5_iter19_a3_verdict.json; CONT ghost_iter19_k0_phase_trellis_adapter_receipt.json; CONT affine_translation_covers_delta2_vert_flip.json. Prior art: 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.