Exact cardinality enumeration for two-neighbour bootstrap percolation on the 8 by 8 grid

Abstract

For the labeled 8 by 8 square grid with open boundaries, exactly 18,158,494,206,600,367,941 initially occupied subsets eventually fill the grid under the two-neighbour bootstrap rule. This note gives all 65 coefficients by initial cardinality and a replayable exact computation. The classical rectangles process yields a triangular recurrence. A polynomial checker verifies 28,954 archived states for 36 rectangle shapes; separate cell and row implementations agree on all totals. Direct propagation on five smaller boards checks every cardinality across 68,222,976 initial subsets. The rectangles-process structure and the minimum-cardinality coefficient 7,006,916 are prior results. The contribution is the complete finite enumeration and its checkable artifact; no worldwide priority or external peer-review claim is made. AI assistance substantially contributed to the derivation, programs, computation, audit, and writing, as detailed in the note. The note and generated data are CC BY 4.0 to the extent applicable rights are held; original code is MIT-licensed. Third-party works retain their own rights.