DCRP88/X72R71: Kelvin Circulation Regeneration Depth and Ancestry Escape

Continuing from DCRP87, which closed work-visibility on the compact class but left the uniform normalized work gap summably convergent because the coarse-grained exhaustion theorem carries geometric weights w_k=r_k/r_0, this round asks whether compact shared-ancestry regeneration can exploit this summability indefinitely; it draws on the Kelvin circulation resupply from DCRP32–33, the native Morrey law from DCRP31, and the 2026 Constantin–Ignatova–Vicol self-similar Weber/Kelvin law (2/5<γ<1/2). It proves that it cannot: compact resolved badness must force a uniform finite family of nonzero circulation atoms (otherwise curl-free plus divergence-free together with the Morrey law would force U≡0, contradicting Ψ^ℓ≥b0). Combined with the strict type-II Kelvin circulation multiplier ρ_Γ=e^{-(1-2γ)S0}<1, the backward ancestry of any circulation atom is amplified by a factor of ρ_Γ^{-n}, so it must exit any compact loop-state class within an explicit finite depth N*=1+⌊log(Γ*/c_Γ)/log(1/ρ_Γ)⌋, and this conclusion is unaffected by the geometrically summable work weights; it further proves that finite loop permutation is impossible (Theorem D88.9). Conclusion: fixed-order badness cannot regenerate indefinitely through a compact material ancestry — any infinite regeneration must repeatedly enter one of the existing terminal channels: tail, filamentation, state, increment, or scale gap — left for DCRP89 to quantify the cost of this first departure.