Noise thresholds of KCBS × KCBS and KCBS × C7 against the almost-quantum relaxation: the window class is tight at Φ(1)

We compare noise thresholds of the products C5⊗C5 (KCBS × KCBS) and C5⊗C7 of odd-cycle contextuality scenarios under local bit noise, for quantum realisations and for the level-1+AB (almost-quantum) relaxation. For the window class, the noncontextuality inequalities supported on the four contexts through one vertex of each cycle, we prove that the level-1+AB threshold equals Φ(1) = (2·2^(1/4) − 2)/(2·2^(1/4) − 1) ≈ 0.2745287, the maximum of the window law; the upper bound is formalised in Lean, and both ends are confirmed by exact rational certificates. Free real representations of the cycles attain Φ(1); on five further near-tight orbits of C5⊗C5 they come numerically within 7.2·10⁻⁸ of it. On the window class, the gap to the regular-ray thresholds 0.2656078 and 0.2634363 is a gap between regular and free measurements, not between quantum and almost-quantum. Pure level 1 gives about 1/2 (violation at 1/2 − 10⁻⁶). For C5⊗C7 we settle 52 of the 63 support classes of facets exactly at one noise value; 11 remain open.