Explicit Diophantine equation provably equivalent to Con(ZFC) constructed, Lean proof in progress
IgorCarron · x · 2026-10-24
Vladimir Reshetnikov has constructed an explicit Diophantine equation whose lack of solutions is provably equivalent (in PA) to Con(ZFC), the consistency statement of ZFC set theory — a concrete instance in the undecidability lineage of Hilbert's tenth problem.
- The equation forms, encodings, candidate expressions, and extensive annotated documentation are public in the ProveIt GitHub repository, along with circuits and tooling.
- The author notes work is ongoing to shrink the equation, and the Lean formalization is not yet complete.
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