HARD PROBLEMS · SEPTEMBER 5, 2026 · EXACT COMPUTATION RELEASED · INDEPENDENT CHECK PENDING
Exactly 18,158,494,206,600,367,941 initial sets eventually fill the 8×8 grid. The release also includes all 65 coefficients indexed by initial occupancy.
The board has open boundaries. A vacant cell becomes occupied when at least two of its orthogonal neighbours are occupied, and the update continues until no further cell can change.
What was computed
The calculation partitions all 264 initial subsets through the rectangular structure of their terminal states and sums the spanning cases with exact integers. It reports both the total and the 65 coefficients for initial occupancies from zero through 64.
Result and boundary
The released computation covers the full finite 8×8 problem. TheoremDB problem P2726 nevertheless remains open, and the submitted record still awaits an independent check. A public preprint and stored computation do not establish peer review, worldwide priority, official acceptance, or a prize award.
Public materials
The Zenodo release contains the paper, reproducibility code, and hashes. TheoremDB record R11849 links the computation to P2726; at present it documents the submission rather than an endorsed resolution.
Contribution note
ChatGPT Pro and Codex made substantive contributions to the computation, code, and initial drafting; Byungwoong Yoo supplied the problem materials, directed the project, and decided the scope of public release.