Have Optical Wigner's Friend Experiments Been Blind to a Geometric Degree of Freedom?

The two published optical Wigner's Friend experiments have operated exclusively at an equatorial measurement geometry (θ = π/2) — a fixed point where every overlap-dependent deformation of quantum measurement statistics vanishes identically (Proposition 1, equatorial cancellation theorem). A single waveplate breaks this cancellation. Re-inserting one quarter-wave plate into the Bong et al. (2020) apparatus tilts the Superobserver measurement to θ = 31°, providing minimum detectable β ∼ 0.075 at 5σ (single-setting) — a search parameter whose methodological role parallels SME coefficients (§II C) — while preserving the Genuine LF violation (8.6σ). A complete survey (Supplemental S1) finds no published implementation has varied this polar angle; only two exist (Proietti 2019, Bong 2020). The theorem constrains the overlap-only class; broader deformation classes (Levels 1–3, §III D) lie outside its scope. Under fair-sampling (η ≈ 0.87), this is a loophole-open screening test; a null δ⟨AB⟩ across a full θ-sweep would falsify the overlap-only class.