The Closure Coefficient, Decided

The Einstein–Cartan spin closure — the statement that an unpolarized fermion fluid contributes a repulsive spin term to the Friedmann equation, ε̃ = ε − λκ(ħcn)² — has carried an underived coefficient since the 1970s. This program's kill-log attack ATTACK-01 derived the closure's form, sign, and density scaling, fixed the ensemble factor g = 1/4, and reduced the remaining uncertainty to a factor-2 lattice: λ ∈ {1/8, 1/4}, the two members differing by an "action dressing," κ versus κ/2. ATTACK-01 named the only input that could decide the fork: derive the effective Friedmann equation from a stated action with spinor conventions fixed end to end. This paper performs that derivation. The action is stated in full, the conventions are fixed before any algebra, the contorsion is solved from those conventions rather than quoted, and every step is executed in a verified symbolic notebook (exit 0). The result decides the fork — and corrects the lattice that posed it. The canonical Einstein–Cartan action, with spin coupled minimally to the connection, gives λ = 1/16 — neither lattice member, but the value ATTACK-01's family had listed only as an extension, with bounce density ρ* = 1.94 × 10⁵⁵ g/cm³, the member closest to Trautman's 1973 printed ~10⁵⁵ g/cm³. A genuinely different action, in which spin couples directly to torsion rather than to the connection, gives λ = 1/4. And Poplawski's printed λ = 1/8 is produced by no extremized action in this family: halving the canonical coupling does not halve λ, it quarters it (to 1/64), because an action-derived coefficient is quadratic in the coupling the extremization eliminates. The lattice's error was bookkeeping — it multiplied the dressing linearly, where any action derivation squares it. The fork is therefore decided twice over: the canonical theory's coefficient is 1/16, and the 1/8 that the literature has carried for fifteen years is a stated number still, now proven to be unstated-action deep.