A 10-state Turing machine that outruns Graham's number

BB(10) > Graham's Number

A new 10-state busy beaver machine, n1, halts from a blank tape with a score exceeding Graham's number. Its behavior is formally verified in Coq without axioms. The machine operates at level ω+1 of the fast-growing hierarchy, surpassing the previous BB(10) champion's level ω. It works by running the BB(8) record's computation, then using a countdown and periodic unpacking to apply the f_ω function a number of times proportional to the BB(8) record's value.