Signed Heat–Curl Cancellation Beyond the Absolute Vorticity Profile

The inverse-scale Dini–Morrey profile closes the absolute vorticity flux but discards all sign and direction. We replace it by the signed heat–curl functional C(ω) = ∫₀∞ ‖curl(e^(sΔ)ω)‖∞ ds. For every finite-energy divergence-free velocity u with Schwartz vorticity ω = curl u, we prove ‖u‖∞ ≤ C(ω) ≤ (4/√π) B(ω) ≤ (4/π²) D(ω), where B(ω) = ∫₀∞ s^(−1/2) ‖e^(sΔ)ω‖∞ ds and D is the Paper-5 absolute profile. The first inequality also holds for distributional vorticity whenever C(ω) is finite. Consequently, the critical L¹-Morrey norm of u ⊗ ω − ω ⊗ u is at most √2 Θ(ω) C(ω), where Θ is the critical L¹-Morrey norm of vorticity. The replacement is genuine: an explicit oscillatory Schwartz family has uniformly bounded kinetic energy and C while both Θ and D grow linearly. The functional nevertheless detects the Paper-4 hidden packet at the required linear rate. Finally, a small scaling-critical L²,¹ time budget for C propagates the Paper-1 Morrey trigger under the stated existing-solution hypotheses. The heat-semigroup estimates are classical; the contribution is the exact obstruction/cancellation calibration in the preceding papers’ normalization. No unconditional regularity claim is made.