The Strong-Coupling Form Theorem: Deriving χ_YM(m_Z) = 2/3 + 1/(4ρ²) and Closing the NICK Ladder

This paper isolates and proves the strong-coupling stiffness theorem of Quantum Traction Theory (QTT) from the Main Book (v10.01, DOI 10.5281/zenodo.17527179). It proves that the Z-boundary Yang–Mills stiffness is not a fitted strong coupling but a forced source form: χ_YM^QTT(m_Z) = 2/3 + 1/(16π²cos²(π/8)) = 2/3 + 1/(4ρ²), with ρ = 2π cos(π/8). The same ρ² = 4π²cos²(π/8) = 33.6969… is the LIA neutrino mass-squared ratio, so the angle is pinned by an independent neutral-sector readout and is not borrowed from the observed strong coupling. The laboratory readout α_s(m_Z) = 1/(4π χ_YM) = 0.11805244792… sits at +0.058σ against the comparator 0.1180 ± 0.0009, which enters only as an audit, never as a constructor input. The proof has five load-bearing parts: L1 derives the birth term 2/3 as triadic transverse colour stiffness; L2 derives the single-rail correction 1/(4ρ²) as the dyadic-gate pullback of completed projected-loop precision; L3 proves uniqueness inside a declared single-correction legal class; L4 quotes the book's Electroweak Stiffness Quantization Conjecture A verbatim and closes its dyadic-quantization factor a_Z² = 1/4 (leaving the dial content D_ρ and the 10/3 tilt explicitly open, as printed); L5 records inheritance, with Λ₃, the string tension, the glueball spectrum, confinement, and the top-edge fingerprint becoming downstream readouts of the forced source. Version 2.0 adds, against the main book: a quantified exclusion overlay in which every excluded form carries its computed pull (including two grammar-illegal forms that land inside the 2σ window, demonstrating that the grammar and not the window selects the survivor); a shared-rail rigidity experiment (centring the strong row drags the neutrino row to −1.31σ); the verbatim Conjecture A closure ledger; the book-printed second-route corroboration via the Artian–UEL gauge-stiffness master matrix, whose color echo α_s = 0.1180526138 agrees with NICK to one part in 7.1×10⁵; a downstream inheritance audit table with DOIs; and a machine-verification appendix reproducing every number from a 25-digit mpmath script. The central falsifier is sharp: exhibit a second axiom-legal single-correction stiffness form, in the declared class, that lands in the physical window without reducing to 2/3 + 1/(4ρ²), and the uniqueness gate fails.