The Strong-Coupling Form and Electroweak Stiffness Quantization Theorems

One projected loop, two gauge-stiffness theorems Can the strong-coupling anchor and the electroweak source ratio be fixed before either laboratory coupling is read? This paper gives two finite source constructions built from the same projected-loop rail, \[ \rho=2\pi\cos\!\left(\frac{\pi}{8}\right), \qquad \rho^2=33.69693720145647\ldots . \] For the strong sector, triadic transverse birth capacity and one neutral dyadic precision pullback give \[ \boxed{ \chi_{\rm YM}^{\rm QTT}(m_Z) = \frac23+\frac{1}{4\rho^2} } \] and therefore \[ \boxed{ \alpha_s^{\rm QTT}(m_Z) = \frac{1}{4\pi\chi_{\rm YM}^{\rm QTT}(m_Z)} = 0.11805244791980282\ldots } \] The resulting readout lies at \(+0.0583\sigma\) against the stated \(\alpha_s(m_Z)=0.1180\pm0.0009\) comparator. The comparator is applied only after the source expression is fixed. For the electroweak sector, the real-\(J\) dial, one-generation charge Gram ledger, and the unique typed one-slot Hadamard recovery give \[ \boxed{ D_\rho = \left\|u+\frac{\rho}{2}Ju\right\|^2 = 1+\frac{\rho^2}{4} } \] \[ \boxed{ \mathsf K_{\rm EW}^{A} = \frac{D_\rho}{8} \begin{pmatrix} 2&0\\ 0&20/3 \end{pmatrix} } \] and hence \[ \boxed{ \chi_2=\frac{D_\rho}{4}, \qquad \chi_1=\frac{10}{3}\chi_2, \qquad \sin^2\theta_W^A=\frac3{13}. } \] The superscript \(A\) marks an undressed Artian source-boundary ratio. The finite dyad-hypercharge camera remains a separate laboratory access operation, \[ \delta_{DY}=\frac{1}{64\rho}, \qquad \boxed{ \sin^2\widehat\theta_W^{\rm QTT} = \frac{3(1+\delta_{DY})}{13+3\delta_{DY}} = 0.231246748695328\ldots . } \] Two complete finite certificates accompany the theorem: one legal dial word from 27 candidates and one legal camera from four candidates. The machine-readable reconstruction reports 20/20 checks passed, including exact rational charge traces, real-\(J\) orthogonality, Hadamard orthogonality, both finite enumerations, the source operator, and the dressed access identity. Core status SIGMA-NICK-STRONG-ANCHOR-SOURCE-CLOSED SIGMA-EW-DIAL-CONTENT-REAL-J-UNIQUENESS-CLOSED SIGMA-EW-MONAD-TO-DYAD-CAMERA-FINITE-UNIQUENESS-CLOSED SIGMA-EW-STIFFNESS-QUANTIZATION-SOURCE-THEOREM-CLOSED Main corpus anchor: Quantum Traction Theory: Main Book v10.01. Reader maps: Lexicon, Derivation Atlas, Corpus Tree, and Two Universes.