Carrier Threads and Mediator Granularity in Finite Legal Reply Systems of Shogi

Fix a sequence of legal shogi checkpoints and, at each checkpoint, a finite fiber of exact ray-tail carriers extracted from all legal replies to a declared candidate move. Pointwise nonemptiness of every fiber, or even nonempty transport across every adjacent pair, does not guarantee that one carrier mechanism persists coherently through the whole sequence. We formalize this distinction by layered carrier systems, forward and backward survivor fibers, and coherent carrier threads. The smallest synchronization obstruction with nonempty fibers and nonempty adjacent transport has profile $(1,2,1)$, and this profile occurs in a standard-reachable shogi game. A mediator assigns finite labels to carriers and declares adjacent transport by label agreement. Refinement deletes transport edges, coarsening adds them, and coarse threads can be certified by the number of newly admitted boundaries they use. For ray-tail carriers we define four observation blocks: actor-channel C, mechanism M, tail shape T, and reply kind K. The full $CMTK$ label is a complete normal form for a rooted, depth-marked ray-tail skeleton, but it deliberately forgets exact moves, absolute squares, physical piece identity, and exact reply-destination depth. Across five complete game records and 597 same-side three-checkpoint windows, $CMT$ is the unique minimal product mediator preserving full-thread existence, and in fact is exact-faithful relative to $CMTK$ on this finite family. A locally legal material-preserving witness shows that the omission of K is not universally safe. We then separate Boolean existence preservation from witness-faithful reconstruction. Coarse false threads are encoded by value-labelled bad cylinders, while the merger of distinct exact threads is encoded by collision circuits. For existence-preserving selective repair, minimal retained block sets are the minimal transversals of a false-thread switch hypergraph; the frontier need not be unique. We give an incremental update rule for this frontier and a distinct update formula for bad cylinders when a new layer is appended. The abstract finite-set and hypergraph facts used here are elementary or classical, but their appearance is not merely an analogy added after the fact. The legal shogi construction supplies a concrete new realization in which transient origin release and terminal re-cancellation generate carrier fibers whose synchronization can be read simultaneously as a layered lifting problem, a local-to-global consistency problem, a relational-join problem, a discernibility problem, and a mediator-repair problem. To the best of the literature search reported here, this is the first formulation of carrier-thread synchronization and mediator repair for complete finite legal-reply systems in shogi, and the first identification of internal-cancellation ray-tail carriers as a concrete shogi realization of layered lifting, local/global consistency, relational-join, discernibility, and transversal-repair structures. The contribution is this cross-domain identification together with the shogi-specific rooted normal form, exact legal certificates, standard-reachable witnesses, locally legal boundary examples, and a reproducible finite atlas.