Discernibility Profiles and Mechanism Repertoires of Legal Reply Systems in Shogi

Abstract

For a fixed legal shogi position and a legal candidate move, consider the complete finite set of legal replies. We observe each reply through three shogi-specific components: actor action edges lost after the reply ($\Lost$), actor action edges newly gained ($\Gain$), and the complete change in pieces in hand ($\Hand$). For every pair of replies, the components on which they differ form a discernibility set. The inclusion-minimal nonempty discernibility sets constitute a \emph{minimal discernibility skeleton}, which determines the complete family of observation reducts by hypergraph blocker duality. We treat each skeleton as a profile symbol. With three observation components, the abstract alphabet contains exactly 19 symbols, and we provide machine-verifiable legal witnesses showing that all 19 are reachable from the standard initial shogi position; hence the bound is sharp on standard-reachable legal play, not merely on abstract information systems. We then factor every legal-reply observation into five local board-and-resource primitives: origin release, destination blocking, capture-step deletion at the destination, expenditure by a drop, and transfer by a capture. This factorization supplies local-mechanism certificates for every minimal discernibility edge. Moving from a chosen candidate to an entire position, we define the latent profile spectrum as the set of profiles realized by all legal candidate moves. Relation-relative endpoint certificates record added, removed, and retained profiles without asserting move correspondence or causal attribution. Finally, we quotient all legal candidates realizing a fixed endpoint profile by a deterministic mechanism signature, obtaining a candidate-complete, edge-selector-relative mechanism repertoire. In a complete audit of six game records, 759 positions, and 63,365 legal candidate systems, 2,374 endpoint/profile systems compress to 4,131 mechanism-signature classes, a factor of approximately 15.34. For same-actor-next comparisons, 1,868 profiles are retained, 1,246 retain their repertoire, and 589 retain the complete signature multiplicity census. Thus multiplicity stability implies repertoire stability, which implies profile retention, while both converses fail. The framework ranks no move, uses no evaluation value, and makes no best-move claim; it studies exact finite distinctions and their certified structural dynamics.