Skelet #17 and the fifth Busy Beaver number — mentioned by LegionMammal978

Sun, 29 Jun 2025 03:07:03 GMT

While that question depends on what you count as an 'enumeration', there's the related question of "What's the richest logic that cannot prove the halting status of all 5-state TMs?" That is, what's the richest logic that some 5-state TM's halting status is independent of? I've pondered that version of the question a bit, but I couldn't get very far due to my lack of expertise in first-order logic. What I do know is that Skelet #17 [0] is one of the toughest machines to prove non-halting on a mathematical level [1], so any theory sufficient to prove that Skelet #17 doesn't halt is likely…

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Skelet #17 and the fifth Busy Beaver number · HackerPapers discussions

Skelet #17 and the fifth Busy Beaver number — mentioned by LegionMammal978