A structural identification of the two-clock projection constant cos(π/8) with the T-gate magic-state overlap and the symmetric CHSH optimum

We give a conditional structural identification, at the level of single-qubit Pauli algebra, between three a priori independent appearances of the half-angle π/8: (i) the two-clock laboratory projection constant of Quantum Traction Theory (QTT), I_clk = cos(π/8); (ii) the modulus of the standard one-qubit T-gate magic-state overlap, |⟨+|T|+⟩| = cos(π/8); and (iii) the symmetric Clauser–Horne–Shimony–Holt (CHSH) variational angle β = π/8 at which the Tsirelson bound 2√2 is saturated. Assumptions. We adopt three structural inputs from QTT (Attar 2025): (A1) a positive-lapse two-clock geometry with a canonical clock-plane refoliation angle θ* = π/4; (A4) a real-dial primitive generator J (J² = −1) with…