The Tube Constitution: Candidate W's Neck Written as Field Equations, and the One Function It Still Owes

Candidate W, the waking construction, has a neck: a flux tube of the axial sector that carries the store's twist. In the waking paper the tube existed as a premise. This paper writes it as field equations: an action (Einstein-Cartan plus a dynamical Nieh-Yan term), the Cartan equations, flux quantization in grain units, the exterior profile, and the stress-energy. It passes the house gates (ghost, tachyon, crossing, degrees of freedom); the sign gate is NOT SATISFIED and no toll is claimed. Two results: Candidate W is narrowed to its shift-symmetric Nieh-Yan member (in a Holst-value dress the storage rate varies 40.48x inside every grain and the drive law's affine pitch collapses), and the phase-slip factor is bounded, A_ps in [0.500, 0.828], S_grain in [4.20x10^35, 6.96x10^35] nats, against 0.017797 nats per grain required. The core is not determined: three zero-parameter completions (Born-Infeld, logarithmic, rational) spread g(1) by 1.66x and core tension by 3.7x. The exact missing piece is one function, the core completion g (equivalently the neck spin-source profile). Verdict: PARTIAL. The vacuum catastrophe is NOT SOLVED; producing-count 0 at derivation grade.