What was already known
The authors distinguish eleven new machine analyses from fifteen rediscoveries of community-known acceleration patterns. The result concerns exact transition descriptions, not a value of BB(6) or a solution of the halting problem.
AI involvement
Gemini 3.1 Pro agents generated patterns, conjectured transition rules, refined and proved them in Lean within a human-built pipeline. The authors report manual validation of final machine, starting-configuration and closure statements, after the autonomous discovery.
Importance
Adds exact mathematical descriptions of previously unanalyzed Busy Beaver holdouts.
Limitations
The paper’s Cryptid classification is provisional and awaits community acceptance. New acceleration rules do not resolve whether these machines halt. Broader repository conjecture-checking machines and other rediscoveries are outside this contribution.
Technical verification
The authors report Lean verification against fixed machine definitions, fixed reachable starting configurations and closed rule systems. The pinned public library states standard-axiom kernel checking; this is source-reported, not a local rebuild. The exact check execution date is not supplied; the paper date is retained separately.
Formal checking
The authors report Lean verification against fixed machine definitions, fixed reachable starting configurations and closed rule systems. The pinned public library states standard-axiom kernel checking; this is source-reported, not a local rebuild.
- Checker
- Authors’ Lean 4 verification
- Scope
- Only the eleven new BB(6) acceleration systems in Appendix A: fixed machine/start definitions, proved transition rules and closure. No general halting or Busy Beaver value claim.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. Manual validation of the final formal statements is documented, but a named human explanation of the central proof for each of the eleven new acceleration systems is not established. Few is the evidence default.
Correction and publication history
Added this sourced contribution with its stated scope, AI attribution, checking evidence and research limits.
Read this published revision