Support-Core Collapse and Boundary Transitions in Admissible Microfabrication Systems

This paper develops a support-core theory of microfabrication limits, with semiconductor scaling as the primary realization. The limiting scale is formulated not as a single material threshold, process threshold, or geometric threshold, but as an admissibility boundary determined by simultaneous material, process, environmental, and device-level constraints. In the registered actuator layer, the theory uses seven support labels: roughness, disorder, bond response, interface-defect response, bulk response, step response, and contact response. Although these labels generate 127 non-empty support combinations, the full registered classification collapses to a finite support core consisting of four minimal feasible generators and five maximal blockers. This yields 72 registered feasible supports and 55 registered infeasible supports. The high-dimensional registered chamber, consisting of primitive coefficients, actuator targets, and requirement coordinates, is shown to reduce to a finite scalar margin certificate. The certified registered stability shell is localized between 0.059 and 0.060. The active upper-side boundary transition is identified with the combined roughness, disorder, bulk, and contact support. The paper then relates this registered support-core shell to geometric scale through a monotone scale-to-burden map, while separating registered admissibility from physical manufacturability. The physical layer is treated as a restriction of the registered layer. Registered infeasibility is inherited physically, whereas registered feasibility requires explicit physical promotion. The resulting physical audit reduces the first-stage transfer problem to five support-level tests. The framework separates finite registered support classification, certificate collapse, scale calibration, and physical realizability without conflating a formal support boundary with a universal physical scaling limit.