An Exoticity–Admissibility Dichotomy for Timelike Kantowski–Sachs–Schwarzschild Junctions

Established spherical-shell theory shows that surface-energy signs depend on the retained regions and their common-normal orientation. This work applies that machinery to timelike junctions between homogeneous Kantowski–Sachs geometry and the increasing-radius Schwarzschild branch and proves a sharp dichotomy at the horizon. For F ≥ 0, every compatible finite-rapidity junction has negative surface density. For F = −f < 0, positive density occurs exactly when the angular curvatures are aligned and f < Ṙ² < (1 + X²)f. Every first-order embedding in this open sector admits local acceleration data for which the intrinsic null, weak, dominant, and strong energy conditions all hold strictly. The admissible acceleration interval is bounded below by the intrinsic 2+1-dimensional strong energy condition and above by the dominant energy condition; the null condition does not bind. Explicit future-infalling embeddings in ingoing Eddington–Finkelstein coordinates realize both density signs through one bulk event, and the positive witness lies at the midpoint pₛ = σ/2. The result is a local thin-shell existence theorem, not a global transition or stability theorem. The record will contain the journal-neutral manuscript, its numbered reproducibility supplement, and a source and verification archive.