Artian's A1-CHSH Spinor-Character Theorem: The pi/8 Clock Projection, T-Gate Magic-State Overlap, and Symmetric Tsirelson Optimum

One basis-invariant half-angle behind the T gate, CHSH, and the QTT clock Why does the same half-angle appear in a quarter-phase gate, the symmetric CHSH optimum, and the QTT two-clock projection? This paper answers the operator question exactly. Starting from the A1 clock-plane quarter-turn and the A4 real-J Pauli representation, the centered clock rotor is \[ U_{\rm A1}=\exp\!\left(-J\frac{\pi}{8}Z\right). \] The positive symmetric CHSH analyzer is generated by \[ U_{\rm CHSH}=\exp\!\left(-J\frac{\pi}{8}Y\right). \] With the Clifford operator \(C=\mathsf S\mathsf H\), for which \(C Z C^\dagger=Y\), the two rotors obey \[ \boxed{ U_{\rm CHSH}=C U_{\rm A1}C^\dagger, \qquad \frac12\operatorname{Tr}U_{\rm CHSH} =\frac12\operatorname{Tr}U_{\rm A1} =\cos\!\left(\frac{\pi}{8}\right). } \] The normalized character is invariant under the basis change. It joins three familiar quantum-information expressions into one exact chain: \[ \boxed{ I_{\rm clk} =\left|\langle +|\mathsf T|+\rangle\right| =\sqrt{P_{\rm win}^{\rm QM}} =\cos\!\left(\frac{\pi}{8}\right), \qquad S_{\max}=8I_{\rm clk}^{2}-4=2\sqrt2. } \] The paper also prints the complete angle ledger: the A1 physical angle \(\pi/4\), the T-gate relative phase \(\pi/4\), the spinor exponent \(\pi/8\), the photon-analyzer parameter \(\pi/8\), the amplitude \(\cos(\pi/8)\), the probability \(\cos^2(\pi/8)\), and the optimal correlator \(1/\sqrt2\) are related but are not interchangeable quantities. The exact identity is a structural cross-lock, not a claim that ordinary CHSH experiments independently validate A1. Standard quantum mechanics already contains the same spinor geometry. A laboratory test is therefore ineligible if \(22.5^\circ\), \(45^\circ\), or the target overlap is programmed into preparation, calibration, control code, or priors. The independent discriminator is the sealed, unprogrammed dual-clock reference-switch test: \[ \boxed{ R_{\rm standard}=1, \qquad R_{\rm QTT\text{-}A1}=\cos\!\left(\frac{\pi}{8}\right). } \] Status CLOSED: SIGMA-A1-CHSH-SPINOR-CHARACTER-IDENTITY NOT CLAIMED: SIGMA-A1-CHSH-INDEPENDENT-EMPIRICAL-VALIDATION PENDING: SIGMA-A1-UNPROGRAMMED-REFERENCE-SWITCH-TEST Version: 2.0 Concept DOI: 10.5281/zenodo.19979594 Author: Ali Attar Website: quantumtraction.org Main-book anchor: Quantum Traction Theory: Main Book v10.01, pp. 235-237, 445-449, 541-542, and 552-553 Independent test: Artian Dual-Clock Sagnac Reference-Switch Preregistration Files Reader-facing PDF, Version 2.0 Reconstruction ZIP containing LaTeX source, style file, numerical verifier, machine receipt, scientific audit, render audit, metadata, and checksums