Artian's A1-Faraday Verdet Reference Theorem: Material Rotation, the Conditional pi/8 Spinor Character, and Finite Terminal-Reference Closure

Can Faraday rotation separate a material response from a terminal-reference clock factor? For a homogeneous, local, optically nonmagnetic medium in linear response, the Faraday angle is fixed by the difference between the two circular propagation indices: \[ Φ_F(ω,B,L) =ω L/2c\,[n_L(ω,B)-n_R(ω,B)]. \] The corresponding Verdet response functional is \[ VM(ω,T) =ω/2cRe [ 1/n_0 .{∂ gM}{∂ B}|B=0 ]. \] Here \(gM\) is the material's gyrotropic off-diagonal response. Its Kubo representation depends on the material Hamiltonian, populations, transition matrix elements, and causal line structure. The Verdet coefficient is therefore a material response packet, not a universal pure number. The paper then isolates a different conditional object. If A1 assigns the source-clock/laboratory-clock plane the quarter-turn \(Θ_A=π/4\), A4's spinor lift gives \[ U_A =exp\!(-Jπ/8Z), c_A =12TrU_A =cosπ/8. \] Version 1.1 closes the four-history exponent with a finite terminal-reference complex rather than an assigned lookup table: \[ 0 C_2^F {D_F}C_1^F {∂_F}C_0^F 0, ∂_FD_F=0, \] \[ κ_F=∂_FTs_F, nab=κ_FTpab, χab=nab^2, \] \[ (χLL,χLA,χAL,χAA)=(0,1,1,0). \] The completed square makes the count independent of whether the same reference conversion is represented at the input or output terminal. In the declared minimal integer-cochain class, the primitive clock cochain is unique up to global orientation. For a detector certified to be homogeneous of degree \(d\) in the affected amplitude, the material-corrected same-sample cross-ratio becomes \[ R_F⁽ᵈ⁾ =exp[-(Δ_K+Δ_N)] √{|{SLASAL}{SLLSAA}|} =c_A^d. \] This yields the frozen paired target \[ Hstd:(1,1,1), HA1:(c_A,c_A^2,1) \] for coherent, unnormalized-power, and normalized readouts. The material functional, conditional A1+A4 character, and finite path exponent are closed at their stated levels. Physical realization of the autonomous Faraday boundary and laboratory execution remain open. Stable anchors Quantum Traction Theory: Main Book v10.01 A1-CHSH Spinor-Character Theorem Absolute-Clock Two-Test Preregistration Absolute-Clock Laboratory Discriminator Atlas QTT Lexicon Derivation Atlas