Arboreal Weinstein Sector Realization for Orbit-Determined Theta Categories on the Non-Archimedean Skeleton:\ Wrapped Descent, Stop Removal, and Finite-Stop Recovery

The previous paper in this branch of the series ArborealMicrolocal2026 showed that, in a simple-wall unimodular arboreal regime, coordinate-free renormalized tail orbits determine a wall-Legendrian atlas \ ^orb S^*B \ on the orbit-recovered non-Archimedean skeleton \ (B\), together with a canonical dg equivalence \ ^₎ₑ₁^ c (B; A_) _ (B) (). \ That result was deliberately microlocal. It identified the orbit-determined theta-category with a compact microlocal sheaf category, but it stopped short of producing an honest symplectic sector whose wrapped category realizes the same object. The present paper supplies that realization. From the same orbit package we construct a canonical atlas of stopped cotangent-Weinstein sectors \ X_^orb=\ (X_, _) \_, X_=T^*U_, \ whose stops are the positive coray lifts of the orbit-recovered wall-Legendrian charts. The first main theorem proves that this sectorial atlas is an orbit invariant, unique up to sectorial Weinstein homotopy. The second theorem is local: by microlocal Morse theory and the arboreal chart package, the compact wrapped Fukaya category of each chart is canonically equivalent to the local theta-chart category \ ( (_) \), with generators given by cocores and linking disks attached to the orbit-recovered stop. The third theorem globalizes these local models by sectorial descent, producing a stopped Weinstein sector \ ( (X_, _) \) whose wrapped category satisfies \ (X_, _) _ (B) (). \ At the same time, stop removal becomes an orbit-readable localization operation on the wrapped category, mirroring divisor removal on the theta side. The fourth theorem is quantitative: on any finite face window and monomial cutoff, finitely many orbit probes recover the truncated stop graph, local generating disks, wrapped continuation functors, and finite stop-removal quotients with explicit asymptotic error bounds. Conceptually, this is the first point in the series where the orbit is shown to determine not only a skeleton, a wall system, or a microlocal category, but an actual Weinstein sector up to wrapped equivalence. The scope is stated sharply: the theorem works in the stably polarized simple-wall arboreal regime and is formulated as a local finite-horizon asymptotic detector, not as a global numerical algorithm under arbitrary noise or for arbitrary non-arboreal stop collisions.