Will we have a proof that an explicit 2-symbol 6-state Turing Machine is the machine that runs for BB(7) steps before halting?
Knowing the exact value of BB(7) might be challenging; it is a very large number, at least 10↑↑15 (a current BB(6) lower bound). It would be impossible to write it down in normal base 10 notation. Bounds using Knuth's up-arrow notation or similar approaches might be loose bounds rather than exact values of BB(7).
For this question, all that is required is that a machine that runs for BB(7) steps be explicitly determined. The machine must be proven to halt, and proven that no other 2-symbol 7-state machine runs for longer. An explicit upper bound or exact value need not be proven.
https://en.wikipedia.org/wiki/Busy_beaver#Exact_values_and_lower_bounds
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