Part III of the "Boundary Rigidity in Fluid Dynamics" Series Constraint-Dependent Phase Randomization and Windowing Sensitivity in Spectral Flux Estimates This work investigates the robustness of spectral energy flux diagnostics under constraint-dependent phase randomization in high-resolution DNS subcubes of isotropic turbulence (Re_λ ≈ 1256). We compare two randomization operators: P0 — component-wise phase randomization PL — Leray-projected phase randomization with shell-matched energy rescaling The study introduces a Δk-matched rescaling procedure and analyzes: inertial-range averaged flux transfer efficiency η divergence diagnostics (Fourier and real-space) windowing sensitivity (no-window, Tukey, Hann) Results show that: Naive phase randomization (P0) significantly alters flux structure. Leray-projected randomization (PL) suppresses artificial divergence but yields near-zero transfer efficiency under strong windowing. Windowing has a first-order impact on flux sign and magnitude in finite subcubes. The work demonstrates that spectral confinement and constraint enforcement fundamentally alter nonlinear transfer diagnostics. It does not claim resolution of the Navier–Stokes regularity problem. Rather, it provides an empirical falsification protocol for phase-coherence-based mechanisms. Together with Part I and Part II, this paper forms a structural progression: Part I — Global regularity under hard spectral truncation Part II — Boundary-induced regularity as structural principle Part III — Empirical constraint-sensitivity in full DNS (that document)