Research · Papers · Direct sums, wedges and the p14 frontier · ML-007
Multiplicative complexity of Pascal and averaging-algebra state-feature classes
Exhaustive search across 2,097,152 Pascal / averaging-algebra state-feature classes yields 7 survivors at mixed-tensor-rank ≤2.
Published 2026-08-29
For everyone
Plain summary
ML-007 tests a specific design route for state features based on Pascal and averaging-algebra constructions. Out of 2,097,152 state-feature classes tested, seven passed a mixed-tensor-rank screen set at ≤2. All seven then failed the next step: none could be built with a single product of raw input bits after the action-feature term. This specific route is EXHAUSTED. The negative result closes this exact path without ruling out broader architectures. The record cites founding dossiers and fleet artifacts, with no dedicated per-entry receipt file or prior-art claim logged.
Result
Exhaustive search across 2,097,152 Pascal / averaging-algebra state-feature classes yields 7 survivors at mixed-tensor-rank ≤2. None of the 7 is realizable via a single raw-input product after the action-feature term. The route is EXHAUSTED.
Setting and definitions
The search space covers the Pascal / averaging-algebra code family partitioned into state-feature classes. The preliminary filter requires mixed-tensor-rank ≤2. The terminal constraint requires synthesizability using one raw-input product following the action-feature term.
Method
All 2,097,152 classes underwent exhaustive rank screening, followed by the single-product synthesis check on the 7 survivors, sourced from founding dossiers and fleet artifacts. No dedicated per-entry receipt file is registered.
Discussion
The exhaustion applies strictly to this feature family and the post-action-feature single-product requirement. It is not a general lower bound or a universal impossibility result. No corrections or prior-art claims are logged; the lack of an individual receipt file remains noted.
For everyone — the takeaway
What this means
This entry records an exact dead end in a search across 2,097,152 options. A first rank filter narrowed the field to seven candidates, and the requirement for a single raw-input product eliminated those seven. Future work can skip this Pascal / averaging-algebra route at this specific stage and focus on other feature families or different circuit arrangements.
Register references
- ML-007
- ZKGOLF-HANDOFF-REPORT.md
- ZKGOLF-RESEARCH-BRIEF-2026-08-12.md
- zkgolf_sha256_continuation/
- 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.