Shell-Weighted Bilateral Estimates for Localized Two-Point Vortex Stretching

We study the symmetric two-point contribution to localized vortex stretching generated by two nested spatial cutoffs 0 <= phi <= zeta <= 1. Their difference is the shell weight w(x,y) = zeta(x)zeta(y) - phi(x)phi(y), which vanishes both on pairs contained in the common core and on pairs with an endpoint outside the outer support. The principal result estimates the shell-weighted angular second moment of the signed Constantin density without any coherence hypothesis: writing a = zeta - phi, f = aomega, g = zetaomega, and letting M_U be the vorticity maximum on the outer support, two parallelism identities applied one endpoint at a time give, for every alpha in [1/2,1], a bound of the shell-weighted angular second moment by 4*M_U times the product of the truncated Gagliardo seminorms of f and g of order alpha/2. Neither a pointwise angular bound nor integrability of a directional supremum is assumed, and no commutator and no isolated cutoff gradient occurs. Interpolation converts the right-hand side into localized energies and dissipations and yields an all-pairs bound for the shell principal. A companion estimate transposes the two-scale low-vorticity budget of the companion manuscript to the same shell, with the architecture and both coefficients taken from there; what the shell weight changes are the two currencies in which the budget is paid. As a thresholdwise application, radial projection onto a vector ball bounds the low-amplitude tails of the bilateral mass and angular moment without a transition-band commutator, furnishing exclusion tests on any prescribed threshold interval bounded away from zero, but no global one-point certificate: the H^1 interpolation envelope necessarily diverges as the threshold tends to zero for every nondegenerate compactly supported configuration. The exact localization remainder falls in the two lower-order kernel classes of the localized representation of Grujic and is estimated on a fixed space-time cylinder in an appendix. No localized enstrophy balance is closed and no regularity conclusion is asserted.