Akari

Query-Relative Soundness of Legal-Reply Compression in Shogi : Quotient Criteria, Canonical Repair, and Action-Edge Counterexamples

Compressing a finite set of legal Shogi replies into coarse classes can reduce the amount of downstream checking, but such compression is meaningful only relative to what is being asked about those replies. We formalize this point as a query-relative quotient condition. For a pos...

Reply-Induced Deletion Geometry in Shogi : Incidence Structures, Fragility Spectra, and Co-Deletion Graphs

We introduce a finite combinatorial structure for measuring how a legal Shogi move's immediate board-influence relation is destroyed by the opponent's legal one-ply replies. For a position $P$ and a legal candidate move $m$, rows index all legal replies and columns index the move...

Reply-Induced Deletion Geometry in Shogi : Incidence Structures, Fragility Spectra, and Co-Deletion Graphs

We introduce a finite combinatorial structure for measuring how a legal Shogi move's immediate board-influence relation is destroyed by the opponent's legal one-ply replies. For a position $P$ and a legal candidate move $m$, rows index all legal replies and columns index the move...

Query-Relative Soundness of Legal-Reply Compression in Shogi : Quotient Criteria, Canonical Repair, and Action-Edge Counterexamples

Compressing a finite set of legal Shogi replies into coarse classes can reduce the amount of downstream checking, but such compression is meaningful only relative to what is being asked about those replies. We formalize this point as a query-relative quotient condition. For a pos...