Arboreal Microlocal Comparison for Orbit-Determined Theta Categories on the Non-Archimedean Skeleton:\ Wall-Legendrian Atlases and Finite-Cell Recovery

The previous paper in this series CategoricalSkeleton2026 reconstructed, from coordinate-free renormalized tail orbits in a positive finite-type regime, a constructible cosheaf of dg categories \ C_^orb \ on the orbit-recovered non-Archimedean skeleton \ (B\), together with a global identification \ _ (B) (). \ That result was intentionally intrinsic: it built a categorical object directly from the orbit but stopped short of comparing it with a genuinely geometric sheaf-theoretic category on the same skeleton. The present paper supplies that comparison in a controlled but nontrivial regime. We work in a simple-wall unimodular setting in which the orbit-recovered wall arrangement on each maximal cell admits an arboreal microlocal model. From the same orbit package we construct a canonical wall-Legendrian atlas \ ^orb S^*B \ and a coefficient system \ (A_\) of completed chart algebras. The first main theorem proves that this wall-Legendrian package is itself an orbit invariant. The second theorem gives a local arboreal comparison: on every maximal cell, compact \ (A_\) -module sheaves microsupported in the local Legendrian chart are canonically equivalent to perfect modules over the completed theta chart algebra. The third theorem globalizes this by descent, producing a canonical dg equivalence \ ^₎ₑ₁^ c (B; A_) _ (B) (), \ so the orbit determines not only an intrinsic theta-category on the skeleton, but also a microlocal sheaf realization of that category. The fourth theorem is quantitative: on every finite face window and monomial cutoff, finitely many orbit probes recover the truncated wall-Legendrian incidence data, local microlocal stalk categories, and continuation operators with explicit asymptotic error bounds. The point is conceptual as well as technical. The orbit does not merely recover an algebra and a skeleton, nor even only a categorical cosheaf on that skeleton. It canonically produces a geometric microlocal model of the same category. At the same time, the scope is stated sharply: this is an arboreal simple-wall comparison theorem, not yet a full wrapped Fukaya comparison or a claim for arbitrary singular wall collisions.