DCRP87/X72R70: Recurrent-Work Unobservability Rigidity Theorem

Continuing from DCRP86's narrowing of the late-stage forest problem to 'does already-resolved CKN badness imply signed pressure-flux work' — an implication left explicitly open in the external 2026 Yu source, owing to possibilities such as pressure-flux cancellation, harmonic pressure tails, coherent low-frequency profiles, leakage, and backscatter — this round proves it, but only on the narrower class of shared-ancestry recurrent-compact solutions, not on the full class of suitable weak solutions. It proves Theorem D87.8 (no-recurrent-work unobservable resolved-bad limit): any configuration that is work-silent in the distributional sense, with local kinetic-energy recurrence and vanishing leakage, must have zero resolved dissipation, forcing the velocity to be spatially constant; if the subfilter residue vanishes as well, the only possible limit is a bulk translation plus an affine harmonic pressure, and the native global Morrey law rules out any nonzero translation — so positive CKN badness on this class cannot coexist with a zero-work detector. Compactness further reduces the infinite-test observability gap to a finite family of active tests, giving an explicit forward-work/backscatter dichotomy. However, it explicitly distinguishes (Theorem D87.14): observability is closed, but the global exhaustion problem is not — the exhaustion inequality's weights w_k=r_k/r_0 are geometrically summable, so even a uniform work lower bound does not contradict an infinite geometric chain — left for DCRP88 to test whether shared-ancestry regeneration can convert this geometrically weighted signed-work budget into a non-summable debt.