Navier–Stokes Regularity Program (Vol. XVIII): Recurrence of Quantile Sparseness and the Barrier Trigger

This record contains Vol. XVIII of the Navier–Stokes Regularity Program. The purpose of this volume is to isolate the **recurrence trigger** needed to activate the barrier mechanism from the preceding modules: quantile sparseness of high-vorticity superlevel sets must reappear frequently enough to prevent sustained interface-driven growth. Main result: we derive a recurrence statement for quantile sparseness using a velocity-form forced–dissipation contradiction based on the Leray energy inequality. The argument shows that persistent thickness of the quantile superlevel set at a fixed geometric scale forces a dissipation level incompatible with the available time-window budget, thereby enforcing recurrence. This recurrence is sufficient to re-trigger the barrier step in the Good/Bad → absorption → recurrence chain. What is included- Main paper (Vol. XVIII): recurrence mechanism, stopping-time logic, and the forced–dissipation contradiction. `Sabljic_NS_Vol18_Recurrence_of_Quantile_Sparseness_Barrier_Trigger.pdf` What this record does NOT claimThis volume does not claim unconditional global regularity by itself. It provides a focused recurrence module intended to be used inside the broader Navier–Stokes Regularity Program. In particular, it does not replace any analytic closure steps needed for the interface suppression estimates and does not introduce numerical diagnostics as logical input to the proof.