The preceding paper in the Weinstein branch proved a finite-resolution theorem for wild completed scattering without a phase gap. On every bounded window, every monomial depth cutoff, and every angular resolution, the renormalized tail orbit determined a resolved packet web, a categorical Stokes groupoid, and a wrapped-theta comparison. That theorem was intentionally formulated as an inverse system over depth and resolution. It did not yet assert the existence of a single exact all-scales scattering object, because once the phase gap collapses one may have infinitely many higher-depth corrections accumulating onto the same packet core. This paper identifies a sharp regime in which the inverse system closes exactly. We assume that the packet contributions across depth are Gevrey--1 and Borel summable: for every stable packet core on a bounded window, the depth-generating series of packet wall functions and packet automorphisms has discrete Borel singular support, simple algebraic-logarithmic singularities, summable action tails, and one-summable Laplace sectors away from finitely many alien directions. In this resurgent wild-completion regime, the orbit determines not just the finite-resolution packet models, but the exact resurgent completion that generates them. The first main theorem is an orbit-to-alien-packet closure theorem. It canonically reconstructs the stable packet cores, the resurgent depth series, the finite Borel action sets, and the bridge operators controlling their alien derivatives. Thus the orbit determines an alien packet web: a scale-free completed scattering object whose finite-resolution shadows are precisely the packet webs of the previous paper. The second main theorem is local and categorical. For every geometric chamber and every non-singular Laplace direction, the median Borel sum of the chamber algebra defines a dg chart category. Ordinary packet crossings and alien ray crossings induce exact autoequivalences; together they generate an alien Stokes groupoid. The corresponding chamber categories and crossing functors assemble into a median schober, and path functors depend only on the associated groupoid morphism. The third main theorem globalizes this picture. The local median charts glue to an exact resurgent theta category and to a median wrapped category of the completed Weinstein sector. Equivalently, the previous pro-system of finite-resolution sectors is shown to be the family of truncations of a single exact resurgent wrapped-theta object. This is the first exact all-scales closure theorem in the Weinstein branch. The fourth main theorem is quantitative. From finitely many orbit probes, finitely many depth coefficients, and finitely many Borel samples on a bounded action disk, one asymptotically recovers the leading action packets, bridge operators, median packet automorphisms, and truncated global category, with error \ O\! (N^-1+N+hR+M+W (R) ). \ Here \ (N\) is the orbit discretization defect, \ (hR\) is the Borel sampling mesh on the action disk of radius \ (R\), \ (M\) is the depth truncation tail, and \ (W (R) \) is the unobserved action tail. Under exponential action decay one obtains the stronger bound \ O\! (N^-1+N+hR+M+e^-cR). \ The scope is again stated sharply. We work on bounded windows, in the one-summable resurgent regime, with discrete action sets and summable alien tails. The paper is not a claim about arbitrary dense Borel webs, unrestricted non-summable chaos, or a globally conditioned numerical algorithm under arbitrary noise. Within its stated range, however, it upgrades wild packet recovery from a finite-resolution inverse system to an exact resurgent scattering theory.
Mohammad Abu-Ghuwaleh (Wed,) studied this question.