DCRP86/X72R69: Hardy Annularization and the Single-Component Work Gap

Continuing from the linear finite-chain bad-scale debt obtained in DCRP85 using a four-term standard cost package (C3,k plus leakage, pressure tail, and PFE residue), this round carries out the forest-budget audit originally planned. The audit finds that D85's usage needs correcting: the actual closed proof of the 2026 finite-chain original theorem uses only the single-component term C3,k (bad scale ⟹ C3,k≥ε3(M)>0); the other three terms, while honest nonnegative ledger entries, have not been independently shown to close CKN badness. Building on this, it derives an exact discrete Hardy identity that converts the heavily overlapping nested-core costs into pairwise-disjoint parabolic-shell debts, proving that the overlap itself can be resolved exactly and is not a genuine obstruction. At the same time, it proves Theorem D86.4 (critical shell additivity NO-GO): the critical model F(r)=cr² shows that the normalized shell debt can diverge even while the physical L³ mass remains finite, so packing alone cannot yield a mandatory global budget. Using the coarse-grained CKN decomposition Ψ(r)≤4Ψ^ℓ(r)+4Ω^ℓ(r), the remaining problem is narrowed to an observability question — whether already-resolved badness can be converted into signed pressure-flux work — left for DCRP87.