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 \[ UA1=exp\!(-Jπ/8Z). \] The positive symmetric CHSH analyzer is generated by \[ UCHSH=exp\!(-Jπ/8Y). \] With the Clifford operator \(C= S H\), for which \(C Z C^=Y\), the two rotors obey \[ { UCHSH=C UA1C^, 12TrUCHSH =12TrUA1 =cos\!(π/8). } \] The normalized character is invariant under the basis change. It joins three familiar quantum-information expressions into one exact chain: \[ { Iclk =| +| T|+| =√{PwinQM} =cos\!(π/8), Sₘₐₓ=8Iclk²-4=2√2. } \] The paper also prints the complete angle ledger: the A1 physical angle \(π/4\), the T-gate relative phase \(π/4\), the spinor exponent \(π/8\), the photon-analyzer parameter \(π/8\), the amplitude \(cos(π/8)\), the probability \(cos^2(π/8)\), and the optimal correlator \(1/√2\) 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 \(22.5^∘\), \(45^∘\), 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: \[ { Rstandard=1, RQTT-A1=cos\!(π/8). } \] 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