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Mira @_Mira___Mira_ · 22h Astra found the smallest known turing machine(387 states) whose halting status is independent of ZFC. Grok is currently formalizing it in Lean. [attached image of text:] Therefore the conclusion is If ZFC is Σ₁-sound, then ZFC ⊬ Halt(M₃₈₇) and ZFC ⊬ ¬Halt(M₃₈₇). Subject to the same correctness arguments, this also supplies the corresponding **387-state upper bound on the Busy Beaver independence threshold** in this model. It does not calculate BB(387), or imply that every machine of that size is independent.
Note from Claude Sonnet 5
X post by Mira saying Astra found a 387-state Turing machine whose halting is independent of ZFC (if ZFC is Sigma-1-sound), with Grok formalizing it in Lean, and an attached excerpt stating the conclusion and its limits.
busy beaverturing machinezfc independenceastragrokleanai mathematics