What Value Forgets: Neural Search Within a Combinatorial-Game Value

Two game positions can have the same exact combinatorial-game value and still differ as compositions. We study fixed-value repertoire construction as a problem in computational creativity. Under a fixed verification budget, we test whether neural search enlarges the certified repertoire available to a composer. Partizan uses a neural acquisition policy to select graph edits for exact verification. An eligible candidate joins only after target equality is proved and its graph quotient is found to be new to that arm’s current stream repertoire. On held-out order-7 Digraph Placement streams quarantined against training and validation candidate and quotient identities, Partizan found 45,863 first-in-stream additions of complete move structures, 35.7% more than equality-only acquisition. A matched ablation found 45,272 with trained novelty, 39,171 before training, and 36,400 with canonical graph distance. The main study recovered 1.050 times as many nonisomorphic graph embodiments as equality-only acquisition (95% bootstrap interval [1.034, 1.069]) and 56.4% more than random selection. Deterministic replay by the released verifier reconstructed all 221,184 proposals and decisions. A bounded transfer study across twelve Domineering values found a smaller gain of 3.42 player-preserving quotients per target and seed (95% interval [0.81, 6.78]) and retained 99.74% of equality-only certified-literal yield. The public atlas lets a composer compare certificate-bound alternatives and choose a representation for further development. Implementation: https://github.com/devinnicholson/partizan Evidence and atlas: https://github.com/devinnicholson/partizan-reproducibility