X72-30: Lock-Budget Recycling and the Trajectory Gap

Continuing from Round 29's critical-lock-work gap (STOP-C33), this round introduces no new lock variables, and instead connects, term by term, the pressure, viscous strain, vorticity dyad, vorticity-direction viscosity, and quotient-gauge forcing needed to sustain the lock back to the existing NS budgets, testing whether a genuinely 'free' source of stabilization exists. The result: the frame supply can be controlled by existing quantities such as ν²‖ΔS‖₂²+‖S‖₄⁴+‖ω‖₄⁴ (the Budget Recycling Theorem), and no new free stabilization mechanism is found; but the real new obstruction turns out to be an Eulerian–Lagrangian gap — a thin-tube concentration witness is constructed showing that a volume-type L^p norm can have ‖F_ε‖→0 while the same function along a particular trajectory has F_ε(X(t),t)→∞, so a positive-volume robust lock can be charged against the global budget, while a measure-zero/thin-tube lock cannot. The route halts at STOP-C34 (budget-recycling / Eulerian–Lagrangian trajectory gap): a critical-mass/capacity/thickness lower bound for a dangerous persistent lock is still missing, passing the baton to the next round to study directly whether the lock-occupation measure Θ_lock must carry positive critical mass.