This is a duplicate of /IsaacKing/what-fraction-of-turing-machines-im-f038c705880f , but with the the Turing machine description specified to be as described in this file: We consider n-state binary tape TMs, where a TM is a 2 by n table, with each entry being a triple consisting of a tape write value, a direction and either a state or the "halt" symbol. This question asks, as n goes to infinity, what fraction of n-state TMs halt when initialized to their first state on a tape of all zeroes.

Resolves once a proof is known that it's within any of these ranges, even if we don't know exactly where in that range. If it seems unlikely that we'll ever narrow it down to a single range but we've at least proven that it's not some of the other ones, I may resolve to multiple.

This is not equivalent to asking for the first digit of Chaitin's constant. Chaitin's constant gives more weight to smaller Turing machines (making the first few digits easily calculable), whereas my question gives more weight to larger machines, asking for the asymptotic behavior as their length goes to infinity.

See also: /IsaacKing/what-fraction-of-turing-machines-im-b4ac02325a4a