Multi-Summable Wild Completion beyond One-Summability for Orbit-Determined Weinstein Sectors:\ Alien-Lattice Schobers, Action Condensation, and Finite-Level Recovery

The preceding paper in the Weinstein branch established an exact all-scales completion theorem for wild scattering under a one-summability hypothesis. On every bounded window the renormalized tail orbit determined an alien packet web, a median schober, and an exact wrapped-theta category, provided the packet depth series were Gevrey--1 with discrete Borel singular support and summable alien tails. That theorem intentionally stopped at the one-level threshold. This paper proves the next and genuinely stronger statement. We allow packet towers that are not one-summable but split into finitely many Gevrey levels after successive accelerations. At each level the accelerated Borel transforms may have not only finitely many core singularities but also directional action-condensation packets: countably many singularities organized along finitely many rays with summable weighted tails. This is the natural regime in which one-summable resurgence breaks, yet exact closure still survives after passing to a finite alien lattice. The first main theorem is an orbit-to-alien-lattice closure theorem. From the orbit one canonically reconstructs the stable packet cores, the ordered Gevrey level set \ 0<k₁<<kᵣ, \ the levelwise core action sets, the condensation directions, the bridge operators attached to isolated actions, and the condensation jets attached to action packets. These data determine a multi-summable alien web whose level truncations recover the finite-resolution packet models of the previous papers and whose rank-one specialization is exactly the one-summable alien packet web. The second main theorem is local and categorical. For every geometric chamber and every admissible multi-direction of Laplace summation, the multisummed chamber algebra defines a dg chart category. Geometric wall crossings and alien ray crossings at each level generate exact functors satisfying a filtered Stokes system: lower-level crossings conjugate higher-level continuation, but only through explicit bridge operators read from the orbit. The resulting chamber categories glue to an alien-lattice schober. The third main theorem globalizes the local picture. On a finite ramified cover recording admissible multi-directions, the local alien-lattice schober glues to an exact multi-summable theta category and to a completed Weinstein sector equipped with a multi-level stop package. These are canonically equivalent. Hence the one-summable wrapped-theta theorem extends to a finite-level multi-summable wild regime with action condensation. The fourth main theorem is quantitative. From finitely many orbit probes, finitely many depth coefficients at each level, finitely many accelerated Borel samples on bounded action polygons, and finite angular resolution separating the visible singular directions, one asymptotically reconstructs the truncated alien lattice, the bridge jets, the median continuation functors, and the truncated global category, with error \ O\! (N^-1+N+ ₉=₁ʳ (ⱼ+hⱼ+ⱼ (Mⱼ) +ⱼ (Rⱼ) ) ). \ Here \ (N\) is the orbit discretization defect, \ (ⱼ\) is the unresolved angular separation at level \ (j\), \ (hⱼ\) is the accelerated Borel mesh, \ (ⱼ (Mⱼ) \) is the depth truncation tail, and \ (ⱼ (Rⱼ) \) is the unseen action tail at level \ (j\). Under stretched-exponential action decay the latter term improves to \ (e^-cⱼ Rⱼ^{1/kⱼ}\). The scope is stated sharply. We work on bounded windows, with finitely many Gevrey levels, discrete core singularities, finitely many condensation directions, and summable weighted action packets. The paper is not a claim about arbitrary dense continuous alien spectra, unrestricted non-summable chaos, or a globally conditioned numerical algorithm under arbitrary noise. Within this range, however, it upgrades the Weinstein branch from one-summable exact closure to finite-level multi-summable exact closure.