Canonical Non-Archimedean Skeleton Reconstruction from Coordinate-Free Renormalized Tail Orbits: Theta Seminorms, Wall-Corrected Degenerations, and Finite-Skeleton Recovery

The previous paper of this series proved that, in a positive finite-type regime, coordinate-free renormalized tail orbits determine the completed theta algebra, the positive potential, the polyhedral filtration, and the compactified mirror package \ (, , W, W, Y, YW). \ What remained open was the genuinely non-Archimedean layer: can the orbit see the Berkovich-type skeleton, the corrected integral-affine base, and the degeneration that collapses the mirror to that base? This paper gives that step, but in a deliberately sharp scope. We work on the positive evaluation cone \ C_+: =\x N_{: x 0 for every active M^+\} \ inside the compact polytope \ (P₁\) defined by the positive potential, and set \ B: =P₁ C_+. \ On this cone the weighted Gauss formula defines an orbit-determined family of multiplicative non-Archimedean seminorms on the completed theta algebra. Their image is a compact rational polyhedral skeleton \ (W Y^\). The first main theorem is an orbit-to-theta-seminorm closure theorem: for each \ (x B\), the formula \ \|ₔ aᵤ zᵘ\|ₓ: =₀㶃 ₀ e^-x{u} \ restricts to a multiplicative seminorm on \ (\), and the orbit determines the whole family \ (\\|\|ₓ\ₗ ₁\). The second theorem shows that these seminorms glue the local toric skeleta of the corrected theta charts into a global compact integral-affine polyhedral complex, canonically identified with \ (B\), and that the bounded analytic mirror retracts strongly onto it. The third theorem is a wall-corrected degeneration theorem. The polyhedral filtration produces a flat Rees family \ W: XW ¹, \ whose generic fiber is the compactified mirror \ (YW\) and whose special fiber is a stratified toric union indexed by the maximal cells of the skeleton. The slab corrections on codimension-one faces are orbit invariants, so the orbit determines not only the central fiber components but also their corrected gluing. The fourth theorem is quantitative. From finitely many orbit probes one reconstructs, on any fixed bounded cell window, the skeleton polytope, the chamber subdivision, the slab functions, and the central-fiber incidence graph with error \ O\! (N^-1/p_*+N+N+N+K). \ If a facet-and-slab separation margin is present, the combinatorial type of the finite skeleton and of the truncated degeneration stabilizes exactly for all sufficiently large \ (N\). Thus, in the stated regime, renormalized tail orbits determine not only the mirror algebra and its compactification, but also the non-Archimedean skeleton on which the mirror collapses and the wall-corrected degeneration realizing that collapse.