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, \[ ρ=2πcos\!(π/8), ρ^2=33.69693720145647… . \] For the strong sector, triadic transverse birth capacity and one neutral dyadic precision pullback give \[ { χYMQTT(m_Z) = 23+1/4ρ^2 } \] and therefore \[ { α_sQTT(m_Z) = {1}{4πχYMQTT(m_Z)} = 0.11805244791980282… } \] The resulting readout lies at \(+0.0583σ\) against the stated \(α_s(m_Z)=0.1180±0.0009\) 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 \[ { D_ρ = \|u+ρ/2Ju\|^2 = 1+ρ^2/4 } \] \[ { KEWA = D_ρ/8 {pmatrix} 2&0\\ 0&20/3 {pmatrix} } \] and hence \[ { χ_2=D_ρ/4, χ_1=10/3χ_2, sin^2θ_W^A=3{13}. } \] The superscript \(A\) marks an undressed Artian source-boundary ratio. The finite dyad-hypercharge camera remains a separate laboratory access operation, \[ δDY=1/64ρ, { sin^2θ_WQTT = {3(1+δDY)}{13+3δDY} = 0.231246748695328… . } \] 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.