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Document BB(6) discovery pipeline and cite arXiv:2610.22603 in READMEs - #8
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| Accordingly, for these machines we look for and formalize **Collatz-like reductions** (`HasCollatzReduction` and `IsValidAcceleration`). Some well-known `BB(6)` cryptids, such as [Antihydra](https://wiki.bbchallenge.org/wiki/Antihydra), are widely considered genuinely hard and have attracted dedicated mathematical research. At the same time, other machines with Collatz-like reductions have subsequently been resolved—either through automated deciders or via number-theoretic methods such as Baker's theorem on linear forms in logarithms (e.g., [`1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---`](https://wiki.bbchallenge.org/wiki/1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---)). It is therefore reasonable to expect that some of the machines in this directory will eventually be resolved as halting (`IsHalt`) or non-halting (`IsNotHalt`) over time, with or without the reductions provided here. | ||
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| The Collatz-like reductions and formal Lean 4 proofs in this library were produced by the Gemini-based agentic discovery pipeline introduced in [*At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier*](https://arxiv.org/abs/2610.22603) (Dos Santos, Veeriah, Havrilla, Bolt, Zuzic, Singh, and Zahavy, 2026). Starting from raw blank-tape execution traces of unresolved `BB(6)` holdouts, the system integrates automated pattern recognition, symbolic conjecturing of recurrent tape configurations (`TapePatternSet`) and piecewise-affine transition rules, informal mathematical reasoning, and formal theorem proving in Lean 4 to synthesize and verify closed-set invariants (`IsClosedPatternSet`) and multi-step accelerations (`IsValidAcceleration`). Using this framework, the pipeline independently rediscovered and formalized reductions for 33 community-documented `BB(6)` holdouts, autonomously discovered and verified 11 novel Collatz-like accelerations reported in the paper, and subsequently uncovered 9 additional novel accelerations (for a total of 53 formalized machines below). |
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mentioning the numbers here might be a cumbersome because we have to update them in the future?
Perhaps we could just refer to the table/numbers below?
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Good point! Removed the hardcoded counts in both BusyBeaver/README.md and README.md and linked directly to the Formalized Machines table below.
mo271
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Oct 19, 2026
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Adds a reference to At the Limits of Computability: Steps Towards Autonomous AI Discovery on the Busy Beaver Frontier (Dos Santos, Veeriah, Havrilla, Bolt, Zuzic, Singh, and Zahavy, 2026) in
README.mdandBusyBeaver/README.md, explaining how theBB(6)Collatz-like reductions and formal Lean 4 proofs were produced and linking to the Formalized Machines table.