DCRP85/X72R68: Scale-Gap Debt and the CKN Finite Chain

Continuing from DCRP84's reduction of the entire Kelvin/trace/line-atom pathway to the old scale-escape coordinate R_scale (adjacent-generation ratio r_{j+1}/r_j→0), and using the DCRP02 interaction graph, the two-sided relative-frequency compactification from DCRP18–20, and the 2026 Yu finite-chain CKN bad-scale counting theorem, this round asks whether this escape is truly a zero-cost geometric degree of freedom. It proves that the scale gap admits two exact interpretations: a UV shell escape from the parent-scale viewpoint, and, from the child-scale viewpoint, an IR escape of that same gap. More importantly, under a uniform global critical bound, every intermediate dyadic bad scale within the skipped band carries a fixed positive standard-channel cost, giving a linear gap debt D_gap≥c(M)(m_j+1) (where m_j is the dyadic gap depth). Conclusion: R_scale is no longer a silent geometric escape but converts into a quantifiable linear finite-chain debt; the remaining question has pivoted from 'classifying another escape route' to 'proving that these repeated channel payments admit a bounded-overlap, mandatory forest budget' — left for DCRP86 to attempt to pack this debt into the PFET/X/tail/state budget and control the overlap.