RESEARCH · RESEARCH · #2178
Gemini-based agentic pipeline autonomously discovers and Lean-verifies new accelerations for 11 Busy Beaver (BB(6)) machines
arXiv:2610.22603v1 presents a Gemini-based agentic pipeline that combines pattern recognition, automated conjecturing, informal reasoning, and formal theorem proving in Lean to autonomously find compact, Collatz-like accelerations describing many execution steps of Turing machines. The system discovered and formally verified novel accelerations for eleven BB(6) machines, provisionally classifying them as "Cryptids"—machines with exact compact descriptions whose halting remains unresolved.
KEY POINTS
- arXiv:2610.22603v1 presents a Gemini-based agentic pipeline that combines pattern recognition, automated conjecturing, informal reasoning, and formal theorem proving in Lean to autonomously find compact, Collatz-like accelerations describing many execution steps of Turing machines.
- The system discovered and formally verified novel accelerations for eleven BB(6) machines, provisionally classifying them as "Cryptids"—machines with exact compact descriptions whose halting remains unresolved.
- Demonstrates autonomous AI integrating LLM reasoning and formal verification to make novel, formally checked discoveries in an uncomputable, open-ended mathematical domain (Busy Beaver).
WHY IT MATTERS
Demonstrates autonomous AI integrating LLM reasoning and formal verification to make novel, formally checked discoveries in an uncomputable, open-ended mathematical domain (Busy Beaver).