Navier-Stokes Triadic Realizability and Channelwise No-Pocket Constraints

This paper isolates a rigorous Fourier-helical component of a broader dissipative-graph programme for three-dimensional incompressible Navier–Stokes. The heat-filtered Reynolds stress tau_s = e^{sΔ}(u⊗u) − e^{sΔ}u ⊗ e^{sΔ}u is a positive same-field covariance whose Fourier coefficients carry the Gaussian mismatch m_s(k,p,q) = e^{−s|k|²} − e^{−s(|p|²+|q|²)} on triads k+p+q=0, with the exact sign relation (−m_s)(p·q) ≥ 0. Combining this filter kinematics with a triad-adapted helical gauge yields closed-form Waleffe geometric factors and, for either ordered heterochiral input pair, a channelwise lower bound with an explicit per-window constant: the no-pocket inequality, stated fail-closed at the channel boundary and delimited exactly by the homochiral escape example. A realizability manifold suitable for later equality-set certification is constructed with semialgebraic (Tarski–Seidenberg) control, and a theorem-level limitation records why the channelwise inequality cannot be read as a bound for the total nonlinear transfer. Third paper of the M-series (M-I…M-V): the projective layer is developed in M-I (doi:10.6084/m9.figshare.33150845) and the canonical covariance and multiplier-class separator in M-II (doi:10.6084/m9.figshare.33151331). The package includes a deterministic verification suite with SHA-256 certificate and provenance notes; the historical origin of the broader programme (Zenodo preprints v14.8 and v7.4) is cited as prior public disclosure only, never as a theorem source.