Completed Scattering beyond Secondary Walls for Orbit-Determined Weinstein Sectors:\ Consistent Mutation Groupoids, Cluster-Schober Atlases, and Finite-Depth Recovery

The immediately preceding paper in this branch of the series SecondaryWall2026 treated the bounded-valence star-unimodular secondary-wall regime. There the renormalized tail orbit determined finitely many secondary corrections, isolated higher-valent stop collisions, and a mutation schober on a finite chamber--joint window. That theorem was deliberately local and finite: it stopped at the first non-arboreal threshold and did not attempt the next closure problem created by scattering completion itself. The present paper treats exactly that next layer. We work in a depth-admissible consistent completion regime. In that regime the completed scattering diagram may contain tertiary and higher walls, but on every bounded polygonal window and at every prescribed monomial depth only finitely many walls appear, the relevant phases remain separated, and the categorical wall operators have bounded spherical rank. The first main theorem proves orbit-to-completed-scattering closure: from the ray-bundle asymptotics of renormalized tail orbits one canonically reconstructs, on every finite window and to every finite depth, the truncated completed scattering diagram together with its wall functions, loop transports, and local stop fronts. The second theorem is local and categorical: each finite completed window determines a canonical mutation groupoid and a cluster-schober chart whose chamber stalks are wrapped chart categories, whose codimension-one continuation functors are simple continuations or spherical/cluster mutations, and whose higher coherences are controlled by the completed scattering relations. The third theorem globalizes these local structures. On every finite-depth cutoff the local charts glue by sectorial descent to a global stopped Weinstein sector and to a constructible cluster schober on the completed skeleton; its global sections agree canonically with both the wrapped Fukaya category of the completed sector and the completed orbit-determined theta category. The fourth theorem is quantitative: finitely many orbit probes on any bounded window recover the truncated completed wall graph, the mutation groupoid, the chamber transport functors, and the finite localization quotients with explicit asymptotic error bounds. Conceptually, this is the first paper in the Weinstein branch of the series where the orbit determines not merely isolated mutation events, but an entire finite-depth noncommutative scattering completion. The scope is again stated sharply: the theorem is proved in a depth-admissible finite-window regime and yields a local finite-horizon asymptotic detector; it is not a claim about arbitrary dense accumulation, arbitrary wild categorical Stokes behavior, or globally conditioned numerical reconstruction under unrestricted noise.