The Vacuum Twist That Isn't There: Propagating Torsion's Fifty-Year Stall, Closed at the Minimal Member

Einstein–Cartan gravity ties torsion algebraically to spin density: where there is no spin, there is no torsion, and a twisted vacuum — background torsion at zero spin density — is not a state the theory contains. For fifty years the field's answer has been to make torsion propagate: the Poincaré gauge program and its descendants. That program has produced a shrinking archipelago of ghost-free parameter subclasses and, to date, no vacuum torsion state from any member. This paper closes the stall at its front door. I take the minimal propagating extension — Einstein–Cartan plus a kinetic term for the axial torsion, one dimensionless coefficient kappa ge 0 — and compute its vacuum completely. With the record's convention that torsion costs positive energy, rho_{mathcal{T}} = bar M_P^2 mathcal{T}^2, the curvature of the potential at the origin is V''(0) = +2bar M_P^2 > 0 at every kappa, and the unique minimum sits at mathcal{T}_{mathrm{bg}}/mathcal{T}_A = 0.000000 for every kappa tested, including kappa = kappa^* = 8.397867×10^{35} and kappa = 10^{40}. The kinetic term gives the twist a way to travel; the potential holds it at zero. Deliverable (a) of the propagating program — a vacuum with mathcal{T}_{mathrm{bg}} neq 0 at sigma = 0 — fails for the minimal member, by the sign. What the closure buys the field is a gate, stated in §5 as theorems-to-be: any deeper member must supply (S) a sign mechanism, (P) a pinning of the condensate as a pure number, and only then (b) the count. The vacuum catastrophe itself is untouched by this paper: NOT SOLVED, printed here so the closure is never spent at the wrong address.