The Factor of Two Is in the Coefficient

My first paper in this corpus, The Aldred Limit, pins the Einstein–Cartan spin-density bound for neutron matter at ρ_A = 9.72 × 10⁵⁴ g/cm³, using the incoherent spin prescription of Böhmer et al., whose coefficient in the spin invariant ⟨S²⟩ = coef·ħ²n² is coef = 1/8. A companion derivation in this program (Wave 2, The Closure Coefficient, Decided) derived the same closure from the canonical Einstein–Cartan action with conventions fixed end to end, and obtained the coefficient λ = 1/16 and a bounce density of 1.94 × 10⁵⁵ g/cm³ — exactly twice mine. That paper decided what the action gives and deliberately spent nothing on the comparison. This paper settles the comparison. I re-derive both densities from their own stated premises inside one convention system, and the answer is: a discrepancy, not a convention. Every symbol the two roads share — the coupling (8πG/c⁴, which my first paper prints as "κ²" and the action derivation prints as "κ"), the per-particle spin ħ/2, the number density n, the neutron mass, and the dust energy density used for both compared numbers — carries the identical value and normalization in both. A convention difference requires a quantity the two systems define differently; there is none left to point at, and I prove it: any redefinition acts on both coefficients through one common factor, leaving their ratio at exactly 2. The factor lives in one named place — the multiplier of the per-particle spin square. The averaging prescription my first paper adopted multiplies (ħ/2)² by 1/2; the canonical action's extremization multiplies it by 1/4. The correction follows: in the notation of The Aldred Limit, the canonical Einstein–Cartan coefficient is coef = 1/16, and the dust balance at that coefficient is 1.94 × 10⁵⁵ g/cm³. My value is not withdrawn: it is the correct output of the dust model at the prescription it declares. What changes is its coefficient's grade — stated, not derived — and the corpus now prints both numbers with their provenance attached. Correcting the matter register does not reconcile them: under the exact Fermi gas the two crossings sit at 1.27 and 5.06 Planck densities, a factor of 4 apart. The discrepancy is in the coefficient, it is exactly 2 there in every register, and it is real.