X72-29: Lock Work and Frame-Forcing Budget

Continuing from Round 28's proven frozen common-lock saddle structure (STOP-C32), this round turns 'how much the additional dynamics must pay to sustain this unstable lock over time' into a computable quantity. It defines the critical strain-gap exposure Γ_ij=∫|λ_i-λ_j|dt as a scale-invariant lock-instability clock, proves a fine-tuning-or-control identity and the lock-work lower bound ∫(-xf)₊dt≳∫gx²dt-ΔE_x, showing that an exactly invariant lock, while possibly existing, is exponentially non-robust; and proves a quadratic strain-gap burden law — for the frame-rotation rate to reach the gap scale |Ω_ij|~g_ij, its numerator must satisfy |N_ij|~g_ij² — yielding the gap-dominant-instability criterion: whenever the stabilizing angular Jacobian is smaller than the gap width, the common lock retains positive transverse instability. The route halts at STOP-C33 (critical-lock-work / frame-forcing-budget gap): whether the forcing budget from pressure, gauge, and the like can be unconditionally supplied by existing energy remains unknown, passing the baton to the next round to connect each forcing channel (pressure, viscosity, vorticity, gauge) individually back to the NS budgets already established in earlier rounds.