Bounded Ownership-Transfer Ranks and Multilayer Strategy Certificates in Finite Shogi Legal-Move Systems

Abstract

We study a finite-horizon reachability problem in finite state systems generated by the ordinary local movement, promotion, drop, and King-safety rules of shogi. A fixed non-king physical token is labelled by provenance, and the terminal event is its first ownership transfer to the opponent. The resulting bounded transfer sets are standard alternating reachability attractors after compilation, but the shogi labels expose several certificate coordinates that ordinary attractor rank does not record. First, we define the antichain of inclusion-minimal physical attacker-token sets supporting a transfer strategy within a given horizon. At the first nontrivial owner horizon, this antichain is exactly the minimal-transversal family of the reply-indexed residual-capturer hypergraph. Regular-turn sparse and hirate-reachable examples separate temporal rank from carrier cardinality: an exact rank-six strategy is carried by one rook, while a hirate-reachable rank-two example requires two distinct attacker tokens. Second, we split finite certificates into active carriers, static support preserving an upper strategy, and static tightness support excluding shorter transfer channels. A regular-turn sparse six-position rook family has constant exact rank six and one active carrier while the number of direct corridor blockers ranges from two to seven. Its upper support is constant, whereas its minimal tightness certificates form growing transversal antichains. Thus temporal depth, active support, minimum static support size, and certificate multiplicity are distinct coordinates. Third, we define branch-anchor cover number, which measures how many action signatures are required to cover the defender's reply branches at a setup layer. Branch width is independent of temporal setup height. We construct a regular-turn sparse rank-four shogi state with noncapturing branch-anchor cover number two and a rank-five promotion-robust gate whose every horizon-optimal first action preserves that width. Finally, we give a regular-turn sparse exact rank-six witness with a forced target-preserving prefix, a unique Dragon gate, and dynamic pin release: a distinguished Gold move is geometrically available but illegal before the gate, then becomes a legal owner branch after the pinning Dragon moves. The verified rank ladder is six, five, four, with branch-anchor cover number two at the final owner node. All lower bounds quantify over the complete canonical legal-move relation of the declared positions. The sparse witnesses are regular-turn local-rule states: ordinary movement, promotion, drop, and King-safety rules are applied to the declared tokens, but omitted tokens are outside the finite subsystem. Except where explicitly stated, material completeness and reachability from the standard initial position are not claimed. The paper contributes a shogi-specific certificate geometry over a known reachability-game backbone, not a new general attractor algorithm.