DCRP92 / X72R75: Finite-Scale Confluence and the Joint Detector

Following DCRP91's reduction of the same-parent material-regeneration problem to a five-term disjunction, this round compresses the first three finite-scale branches (fixed-relative filtered-vorticity activity, the D26 SGS recurrence detector, and scale-gap debt) into a single joint detector vector J. It proves that on the compact same-parent material-regeneration class, the ℓ∞ norm of J must have a positive lower bound, and a finite-coordinate pigeonhole argument then shows that some fixed detector coordinate must recur with positive density at least 1/(M_J N*), so the survivor can no longer evade this indefinitely by switching defect types. The round states plainly that this does not yet amount to a global exhaustion contradiction — the detector can recur at positive density while still paying only a geometrically summable physical cost — leaving the next round to address the relationship between positive-density finite-detector recurrence and non-summable regeneration debt.