X72-31: Persistent-Lock Occupancy Capacity Problem

Picks up the gap left by Round 30 (STOP-C34: the Eulerian bulk L^p budget cannot directly control a single Lagrangian trace), and asks whether a persistent lock can occupy zero critical mass while still carrying a fixed share of the dangerous supply. Proves the Source–Occupancy Lemma by Cauchy–Schwarz, μ(A)≥β²/𝔍_W, and establishes the Vanishing-Occupancy Singularization Dichotomy: if a fixed source share corresponds to a vanishing occupancy measure, then either the participation ratio 𝔍_W must diverge, or the source becomes singular relative to the carrier measure. Under bounded source participation, Round 30's trace gap can be closed conditionally; the new gap STOP-C35 (Persistent-Lock Occupancy/Singular-Concentration Gap) is handed to the next round's source-participation dynamics.