Canonical Kernel and Theorem Sheet of the Finite-Capacity Latency–Erasure Theory Unified Variables, Recovery Limits, Source Hierarchy, Admissibility Conditions, and Cross-Sector Consistency for a Multi-Regime Effective Physical Program

We present the canonical kernel paper of the finite-capacity latency–erasure theory (FCLET), designed to freeze the common mathematical backbone underlying its weak-field, cosmological, perturbative, wave-propagation, thermodynamic, strong-field, laboratory, and microphysical sectors. Earlier FCLET manuscripts developed these sectors in substantial detail, but the program now requires a single notation-stable, theorem-oriented reference document that states the shared variables, recovery limits, source hierarchy, admissibility conditions, descendant maps, and branch logic in one place. The present manuscript provides that reference. The purpose of this paper is not to replace the sectoral papers, but to prevent cross-paper ambiguity. We define the canonical latency variable, the bounded load map, the proper-time law, the source decomposition, the effective parameter vector, the recovery branch, the strong-field saturation branch, and the microphysical-to-macroscopic reduction map. We then formulate the core admissibility conditions—kinetic positivity, bounded load, recovery continuity, screened weak-field regularity, perturbative stability, radiative cleanliness, thermodynamic non-negativity, and strong-field matching discipline—and collect them into a theorem-style consistency sheet. We also define the precise meaning of trivial survival, nontrivial survival, exclusion, and cross-sector failure. This manuscript is intentionally critic-facing. It is written to answer the strongest structural objection to a large research program: that too many sectoral papers may create the appearance of unity without a frozen mathematical core. The present work removes that objection by providing one canonical kernel, one parameter dictionary, one admissibility architecture, and one branch taxonomy for the entire FCLET corpus. Keywords: effective theory, canonical variables, admissibility, recovery limit, source hierarchy, modified gravity, finite-capacity universe, theorem sheet, branch structure, FCLET