Planetesimal formation must cross two barriers at once: a physical barrier, whereby aerodynamic radial drift removes pebble-sized solids on 102—103 yr timescales, and a computational barrier, whereby resolving the three-dimensional turbulence that concentrates those solids imposes Courant-limited time steps that make Myr integrations intractable. We present a stochastic—subgrid framework that advances the mean flow and grain growth deterministically on macroscopic (∆t ∼ 10—100 yr) stepswhile injecting the unresolved, intermittent turbulent concentration as samples from a variance—gamma (VG) Lévy process embedded in an Ornstein—Uhlenbeck relaxation. A single intermittencyparameter ν — the excess kurtosis of the turbulent fluctuations, tending to the Gaussian limit as ν → 0 — controls the rare, fat-tailed bursts that trigger streaming-instability-mediated gravitational collapse. The closure is deliberately falsifiable: ν inferred from magnetohydrodynamic (MHD) turbulence should increase with magnetic activity and vanish in dead zones, and the excess kurtosis of coarse-grained increments should decay as κexc ∝ ∆t−1, the signature of Lévy aggregation.We develop the model through an analytic collapse rate with a continuous mass function, a one-dimensional radial open system with grain growth, drift, diffusion and pebble supply, imposed andthen self-consistently generated pressure traps, and an explicit, spatially-resolved convergence field. The mass-conserving model yields sharp, testable results: in a realistic drifting disk the concentration breach occurs in the far tail where the Gaussian probability is < 10−10, so intermittency is a prerequisite for planetesimal formation (the yield rises ∼ 30× from ν = 0 to ν = 2); a self-consistent dead-zone edge — derived, together with the turbulence strength and intermittency, from a singlemagnetic-activity profile — produces a surface-density bump that localizes formation and makes itν-independent, while the adjacent smooth region is ν-controlled, so intermittency and pressure traps are complementary and govern distinct regions. We compile seven predictions and, because MHD data are not yet in hand, present the verification methodology rather than its outcome: a pipeline that extracts the intermittency map, the aggregation exponent, and the convergence-to-velocity kurtosis ratio from any velocity field, validated on realistic synthetic surrogates, together with de-cision tables that fix in advance which measured outcome would refute the framework and whichwould robustify it. We position the framework honestly with respect to the turbulent-concentration and streaming-instability literature: the concentrating mechanism is inherited, while the Lévy closure, the macro-step integrator, the falsifiability design, and the self-consistent trap—intermittencydichotomy are new.