Research · Papers · Cipher S-boxes, χ, and quantum gate counts · ML-018
Exhaustion of the 3-gate full-domain start on the Toffoli acyclic p7 route
Real 3-gate full-domain start on Toffoli acyclic p7 route: EXHAUSTED after 786,430 factor checks; alternate prefixes: UNKNOWN
Published 2026-08-29
For everyone
Plain summary
This entry records the closure of a search route for reversible logic synthesis. The register labels this path the Toffoli acyclic p7 route, where acyclic indicates a cycle-free layout and p7 is an unspecified route tag. A Toffoli gate flips a target bit when both of its control bits are 1. The search targeted a real 3-gate prefix intended to operate across the full input domain. After testing 786,430 candidate factor splits without success, the route was declared dead. Alternate prefixes were not evaluated and remain recorded as UNKNOWN. Route status: EXHAUSTED. The register provides no evidence, solver outputs, proof certificates, replay scripts, written derivations, or prior-art citations for ML-018.
Result
The real 3-gate full-domain start on the Toffoli acyclic p7 route is dead after 786,430 factor checks. Alternate prefixes remain honest UNKNOWN. Status: EXHAUSTED.
Setting and definitions
- Toffoli acyclic p7: designated cycle-free route; p7 is undefined in the register.
- 3-gate full-domain start: a three-gate initial segment operating on the complete domain.
- Factor check: evaluation of a candidate circuit decomposition split.
- Prefix: candidate initial gate sequence.
- Status values: EXHAUSTED denotes the closed route; UNKNOWN denotes unevaluated alternate prefixes.
Method
The register logs 786,430 factor checks terminating in a dead route, with alternate prefixes left at UNKNOWN. It names no encoding formulation, solver, certificate, replay pipeline, written argument, or receipt artifact. Evidence: none stated.
Discussion
The exhaustion applies strictly to the Toffoli acyclic p7 route. Because alternate prefixes remain UNKNOWN, this finding does not imply a global impossibility result across all configurations. Corrections: NONE (the INDEX corrections list contains no ML-018 entry). Prior-art position: none stated. Status: EXHAUSTED.
For everyone — the takeaway
What this means
A specific cycle-free search path was abandoned after 786,430 candidate splits failed. This result does not prove that a three-gate start is impossible overall, since other initial prefixes were never tested. The p7 path is marked EXHAUSTED, while those untested starting branches remain UNKNOWN. The register contains no log files or verification receipts to independently retrace the checks.
Register references
- ML-018
- Receipt artifact: the register does not record this.
- 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.