The preceding paper in the Weinstein branch of the renormalized-tail program treated the depth-admissible consistent completion regime: on every bounded polygonal window and at every fixed monomial depth only finitely many walls were visible, a positive phase gap separated distinct wall directions, and the orbit determined a finite mutation groupoid together with a cluster-schober atlas. That theorem deliberately stopped before the first truly wild phenomenon. Once the phase gap collapses, completed walls can accumulate on limit directions, higher-order corrections can condense into packets, and categorical continuation is no longer controlled by a finite chamber graph alone. A referee can therefore ask the next question immediately: does the renormalized tail orbit still determine a coherent scattering object when completed walls accumulate and no positive phase gap is available? This paper gives a precise positive answer in a resolution-admissible wild completion regime. In that regime the completed scattering pattern may have infinitely many walls on a bounded window, but for every window \ (W\), depth cutoff \ (D\), and angular resolution \ (>0\) the walls of depth at most \ (D\) cluster into finitely many packets. Each packet has a well-defined core direction, summable wall mass, bounded local categorical rank, and controlled residual inconsistency. The first main theorem proves orbit-to-accumulation-web closure: from the ray-bundle asymptotics of the renormalized tail orbit one canonically reconstructs, for every \ ( (W, D, ) \), the truncated packet web, the packet wall functions, the resolved chamber complex, and the limit-direction data. The second theorem is local and categorical. It associates to every resolved window a categorical Stokes groupoid and a web-schober chart whose chamber stalks are wrapped chart categories and whose packet crossings induce cumulative continuation or mutation functors. Path functors are shown to depend only on the corresponding morphism in the Stokes groupoid. The third theorem globalizes these local structures. On each finite-resolution cutoff the local charts glue, by sectorial descent, to a completed stopped Weinstein sector with accumulation stops, and to a constructible web-schober on the resolved 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 a bounded window recover the resolved packet web, the categorical Stokes generators, the chamber transport functors, and the finite localization quotients with explicit asymptotic error bounds of the form \ O\! (N^-1+N^-D+ₖ, ₃ () ), \ where \ (N\) is the orbit-discretization defect and \ (ₖ, ₃ () \) is the unresolved packet mass below resolution \ (\). Under exponential packet concentration this becomes \ (O (N^-1+N^-D+e^-c/) \). Conceptually, this paper is the first point in the Weinstein branch where the orbit determines a genuinely wild scattering system: not merely isolated mutation events or a finite completed diagram, but a scale-resolved accumulation web together with its categorical Stokes transport. The scope is again stated sharply. The theorem is local in the window, finite in depth, and finite in resolution; it is not a claim about arbitrary dense accumulation, unrestricted higher-codimension chaos, or a globally conditioned numerical algorithm under arbitrary noise.
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Mohammad Abu-Ghuwaleh
Zarqa University
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Mohammad Abu-Ghuwaleh (Wed,) studied this question.
www.synapsesocial.com/papers/69e1cffa5cdc762e9d85909d — DOI: https://doi.org/10.5281/zenodo.19589291