The Curl Cannot Face Forward: The Vector Spin Momentum at the Degeneracy Surface, and Why the Velocity Stays Unassigned

Completes paper #367's proof against the whole spin tensor. Paper #367 proved the scalar spin momentum identically zero (incoherent averaging; the Frenkel condition killing the electric components, the magnetic part entering only as a curl) and left the curl itself standing in its own sector; the decision record of 2026-11-03 queued that vector-sector object as honest work. Gated digit-for-digit on #367's exhibits (required scalar spin momenta -3.4481 incoming and +0.1903 outgoing at the surfaces x = 1/2, Q = +3.6490 / -0.2014, the electric combination +10.9471 / -0.6041, 4 pi G a0^2 = 1.0583) and on #356's surface data (w_eff = -1, enthalpy x(1-2x) = 0 at x = 1/2, Frobenius exponents 0 and 2, transfer determinants 1.0000). The curl operator on a Fourier mode has eigenvalues 0, +ik, -ik: invertible on the transverse plane with inverse -(k x)/k^2, identically zero on the longitudinal line, and blind to the spin vector's own longitudinal part (an amplitude with longitudinal component 999 returns its target transverse curl exactly). The vector momentum constraint at the degeneracy surface therefore reduces to alpha (curl ds)_i = -0.9449 Q_i^T in rho_A units, with alpha nonzero and convention-dependent: closure in form is permitted at every k != 0, forbidden for the homogeneous mode, and for #356's worked scalar solution the condition reverses sign and requires the curl itself to vanish at both surfaces. In value the frame owns nothing to spend: the vector term is linear in the spin tensor, coarse-graining commutes with the curl, and the forced incoherent prescription gives its mean as zero, while as a coherent Frenkel-allowed field its value is unowned and ungoverned by any owned equation. The scalar verdict does not move: the longitudinal projection of any curl vanishes identically (scan maximum 1.4e-16), so no vector spin momentum at any amplitude supplies the scalar requirement, and v_eff remains unassignable at rho = rho_A/2, now proved against every component of the spin tensor, each failing for its stated reason. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.