A Weighted Triadic Connectivity Barrier for High-Wavenumber Propagation in Finite ThreeDimensional Navier-Stokes Dynamics

High-wavenumber propagation is a necessary component of any spectral-runaway scenario for the threedimensional incompressible Navier-Stokes equations. A previous dual-barrier framework separated thisissue from critical-tail dominance by introducing a dyadic propagation factor gamma_R and a dissipationnormalized tail ratio Psi_R. The remaining question was why strict dyadic contraction should occurdynamically rather than merely being assumed. Here we introduce a scale-to-scale weighted triadicconnectivity diagnostic C_R. For each output mode k, individual Leray-projected triadic contributions aresummed in norm before same-output cancellation to define a potential feed P_R, while their vector sumdefines the realized feed F_R. Writing G_R=F_R/P_R gives the exact finite-dimensional decompositiongamma_R=C_R(G_2R/G_R), where C_R=P_2R/P_R. Because all projected triadic contributions scalequadratically with velocity amplitude, C_R is amplitude-invariant. In direct finite Fourier tests, spectrallocalization produced a reproducible collapse of C_R and a corresponding suppression of gamma_R.Across 450 static states spanning two truncations, multiple cutoffs, three spectral-envelope families, andmatched seeds, the ordering localized < intermediate < broad held for both C_R and gamma_R in 150/150matched comparisons; Spearman rho(gamma_R,C_R)=0.99884. In a separate finite Navier-Stokes timeevolution test with 124 modes, 6486 resolved ordered triads, 48 trajectories, and 528 sampled states, thesame ordering persisted in 176/176 matched time comparisons, with rho=0.98227 (bootstrap 95% interval0.97654-0.98596). These results support a candidate mechanism in which spectral localization depletes theweighted set of triadic routes capable of feeding the next dyadic shell, thereby suppressing realized highwavenumber propagation. The result is a finite-dimensional mechanism and diagnostic, not an infinitedimensional regularity theorem. Keywords: Navier-Stokes equations; Fourier triads; spectral cascade; triadic connectivity; spectrallocalization; high-wavenumber propagation; geometric depletion A dataset for reproducing this study is also included.