Deciding hard small Turing machines (Busy Beaver)
Prove halting or non-halting of specific small Turing machines that current deciders cannot resolve.
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Open problems
Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
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