The Two-Point Strain–Direction Pairing for Unmodified 3D Navier–Stokes

The two-point strain–direction pairing on unmodified Navier–Stokes ends at CCZ M(t) |δξ|2 + remainders. Replacing the coefficient by an M-independent −γ is equivalent to the regularity problem. On unmodified 3D incompressible Navier–Stokes the geometric-kernel expansion of the two-point pairing stops at CCZ M(t) |δξ|2 + RA + RB + RC. The leading coefficient is sharp on intermediate-axis alignment. Remainders (A)–(C) do not cancel it. This note does not replace the coefficient by an M-independent −γ and does not discharge Constantin–Fefferman / Definition 7.1. Related: 10.5281/zenodo.22240168.