Secondary-Wall Mutation beyond the Arboreal Regime for Orbit-Determined Weinstein Sectors:\ Higher-Valent Stop Collisions, Schober Descent, and Finite-Joint Recovery

The immediately preceding paper in this branch of the series WeinsteinSector2026 proved that, in the simple-wall unimodular arboreal regime, coordinate-free renormalized tail orbits determine a canonical stopped Weinstein sector \ (X_, _) \ whose wrapped Fukaya category realizes the orbit-determined theta category. That theorem was intentionally sharp: it covered simple walls, arboreal Legendrians, and stop-removal localization, but it excluded the first genuinely coupled phenomenon beyond that regime, namely higher-valent stop collisions created by secondary wall scattering at codimension-two joints. The present paper treats precisely that next layer. We work in a bounded-valence star-unimodular secondary-wall regime, in which primary wall data are still orbit-visible but joint scattering produces finitely many secondary walls and local non-arboreal stop collisions. The first main theorem proves orbit-to-secondary-wall closure: from the ray-bundle asymptotics of renormalized tails one recovers, on every finite window, the secondary wall arrangement, the joint scattering words, and the homotopy class of the local higher-valent stop model. The second theorem is local and categorical: each isolated higher-valent joint determines a canonical mutation schober whose chamber stalks are wrapped chart categories, whose singular stalk is a joint category generated by cocores and joint-linking disks, and whose transition functors across secondary walls are spherical mutations. The third theorem globalizes these local models. We glue the higher-valent local sectors by sectorial descent and obtain a constructible schober of dg categories on the orbit-recovered skeleton, together with a canonical equivalence between its global sections, the wrapped category of the global mutated sector, and the orbit-determined corrected theta category. The fourth theorem is quantitative: finitely many orbit probes on any bounded chamber--joint window recover the truncated secondary wall graph, mutation matrices, spherical ranks, and finite localization quotients with explicit asymptotic error bounds. Conceptually, the paper is the first place in the series where the orbit determines not only a Weinstein sector and its wrapped category, but also the categorified mutation data forced by higher-valent stop collisions. The scope is again stated sharply: the theorem concerns the bounded-valence star-unimodular secondary-wall regime and is formulated as a local finite-horizon asymptotic detector, not as a global numerical algorithm under arbitrary noise or for arbitrary wild non-arboreal collisions.