The Exact Running Times of the Busy Beaver Records for BB(6), BB(7) and BB(3,4): a Lean 4 Formalization with Their Last 200 Digits

Three of the four machines treated here hold the busy-beaver record of their class today; the fourth held the BB(7) record until October 2026. Each record is published elsewhere as a lower bound.

This deposit gives the exact step count of each machine's first halt, proved in Lean 4 on the standard axioms, with its last 200 decimal digits, and four standalone Python checkers that rebuild each machine from its rows and recompute the digits.

To our knowledge these are the largest numbers ever proved to be the exact running time of a computation.

To verify: run "lake exe cache get" then "lake build", and run each program in verify/.