Direction of vorticity in 3D Navier–Stokes: closed identities, a geometric reduction, and a scale-sharp remaining estimate

This note records what a coadjoint-tether construction actually yields for the 3D incompressible Navier–Stokes equations, and what it does not. What it proves. Degeneracy of the tether pairing leaves vorticity transport classical. The projected kernel is a real symmetric bilinear form, not Poisson and not sesquilinear. Closed identities: Jacobian of the vorticity direction ξ, the direction equation, the spatial-maximum law, the Constantin–Fefferman kernel bound, Young at viscous scale returning Beale–Kato–Majda, and the Lyapunov source signs. Energy plus Calderón–Zygmund on L2 place the stretching reaction Pξ(Sξ) in L2t L2 without ‖ω‖∞. Parabolic scaling is an obstruction at energy regularity (p=2 is below p>5/2). The implication "Definition 7.1 ⇒ T*=∞" is the theorem of Constantin–Fefferman and Beirão da Veiga–Berselli, not a new regularity proof. What it does not prove. Definition 7.1 (uniform-in-T* Hölder-½ of ξ on {r≥Ω}); Clay Millennium global regularity; a blow-up example; a sesquilinear or Hermitian structure; remaining lemmas (A) integrability upgrade or (B) Campanato on 4sin²(φ/2). This is a geometric reduction and a retirement of false closing paths. It is not a Clay solution.