FOURFOLD SOLENOIDAL DETECTORS AND SHARP SEVEN-RAY STRESS-CONE BOUNDS FOR UNFORCED NAVIER–STOKES CARRIERS

We derive two complementary restrictions on compact, anisotropically shrinkingcarriers for the three-dimensional unforced incompressible Navier–Stokes equation. First, for asmooth fourfold-equivariant carrier satisfying specified similarity and residual bounds, its nonzeroleading axial angular-advection profile admits an explicit compact divergence-free detector. Anyexact unforced correction with vanishing relative local L2 mass must consequently obey aquantitative amplitude–concentration inequality. At the representative similarity exponenth = 1/10, a correction with relative mass O(τ 1/10) must attain velocity amplitude at least oforder τ −7/10. Second, we determine the exact hexagonal axial–azimuthal projection of a seven-rayone-sided positivity cone, including a rational feasible lift at every vertex. Full cylindrical stressdivergence, pressure-compensated flux identities and the moving-frame connection formula explainhow these algebraic restrictions enter a physical source equation. Exact rational computationsand independent symbolic integration certify the finite polynomial constants. These resultsare conditional geometric and analytic restrictions; they do not construct a finite-time singularunforced Navier–Stokes solution.