Strongly Solving Churn on the Recommended Size-3 Board

This archive accompanies the article "Strongly Solving Churn on the Recommended Size-3 Board" (Brun, 2025, submitted to ICGA Journal). It contains the source code, strategy certificates, and independent verifier supporting a complete computational solution of Churn on its recommended size-3 hexagonal board. ## Game Churn is a finite two-player placement game designed by Mark Steere in December 2024. Players alternate placing stones on a hexagonal board, with mandatory isolated placement when possible, smallest-group placement otherwise, and compulsory removal of all friendly groups smaller than the newly formed group. The published rules recommend the size-3 board (19 cells) and specify use of the pie rule. ## Results Fixed-colour game: Red wins from the empty board in 87 plies by opening at the centre. Pie-rule game: Player 2 wins. The size-3 board has four inequivalent first moves under the D6 symmetry group of the hexagon; for each of these, Player 2 can choose the winning colour. The reachable D6-canonical state space contains 56,648,788 states. ## Contents - Churn_rules.pdf — original rulesheet by Mark Steere (included by permission of the rulesheet's open licence)- README.txt — usage instructions and reproduction protocol- SHA256SUMS.txt — integrity hashes for all files in the archive- verification_log.txt — log of successful independent verification of all five certificates- churn_solver_v3_piecerts.cpp — solver source code (C++)- churn_cert_verify.cpp — independent verifier source code (C++), written separately from the solver- churn_root_cert.tsv — strategy certificate for the fixed-colour game from the empty board (411,272 states)- churn_pie_cert_orbit1_BLUE.tsv — pie-rule certificate, orbit 1 first move, Blue wins (492,285 states)- churn_pie_cert_orbit2_RED.tsv — pie-rule certificate, orbit 2 first move, Red wins (534,766 states)- churn_pie_cert_orbit3_BLUE.tsv — pie-rule certificate, orbit 3 first move, Blue wins (351,044 states)- churn_pie_cert_orbit4_RED.tsv — pie-rule certificate, orbit 4 first move, Red wins (411,271 states) Total uncompressed size: 140,072,576 bytes. ## Reproduction The solver regenerates the full tablebase in memory and exports the five strategy certificates. The independent verifier reads the certificate files, reconstructs legal moves from the rules, applies removals, checks terminal positions, follows the certified move at winner-to-move nodes, and enumerates all legal replies at loser-to-move nodes. The verifier does not consult tablebase values, so it confirms the exported certificates independently of the tablebase construction. Compile with a recent C++17 compiler (g++ 9 or later, clang 10 or later). See README.txt for exact invocation. Expected verification output is reproduced in verification_log.txt; SHA-256 hashes in SHA256SUMS.txt allow integrity checking against the deposited files. ## Citation If you use this archive, please cite both the article and the dataset: Brun, C. (2025). Strongly Solving Churn on the Recommended Size-3 Board. ICGA Journal (in press). Brun, C. (2025). Churn (size 3) — solver, strategy certificates, and independent verifier [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.20096036