215-state Turing machine proven to halt iff ZFC is inconsistent, verified in Metamath Zero
teortaxesTex · x · 2026-10-24
Mathematician Elliot Glazer announced a machine-checked proof in Peano arithmetic, formalized in Metamath Zero, that the 215-state Turing machine K215 halts if and only if ZFC is inconsistent. K215, discovered by @ereliuereteer, encodes Glazer's single-schema set theory K. The repo pins the exact theorem statement with a sha256 hash, defines halting via the literal transition table from a blank tape, and encodes inconsistency as a numerically coded ZFC proof of falsity — a Busy Beaver-style construction tying halting to set-theoretic consistency.
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