DCRP99 / X72R82: X72–Kelvin Bounded-Lag Synchronization

Following DCRP98's reconvergence of the dual-lock conveyor into X∨N∨T, and using DCRP62's N⟹X∨T to simplify it to C_dual⟹X∨T, this round uses compactness to upgrade DCRP76–79's qualitative conclusion that no infinite compact X-free material chain exists into a quantitative, uniform finite X-hitting horizon L_X and detector gap c_X>0. It further points out that both X recurrence and DCRP95's Kelvin phase slip are syndetic clocks, but positive density alone does not imply they co-occur at zero lag — a correction to the zero-lag assumption implicit in the DCRP96–98 analysis. Using a finite-lag/detector/orientation pigeonhole argument, it proves that a fixed Kelvin-slip coordinate and a fixed X72 detector co-recur at a fixed lag ℓ* on a positive-density set; the surviving paradigm is finally compressed into the bounded-lag X72–Kelvin lock conveyor, leaving the next round to determine whether this lag corresponds to a genuine causal transfer kernel.