Participatory horizons and the CMB parity anomaly: a smoothed antipodal evidence operator

The CDM model accounts for the cosmic microwave background with remarkable precision, yet persistent anomalies at the largest angular scales remain unexplained. Among these, the low-multipole temperature spectrum exhibits an even/odd parity asymmetry at the 0. 2--0. 3\% level across 30. This programme hypothesises that such anomalies reflect the observer's causal diamond acting as a recording aperture on the observed sky, while retaining CDM as the underlying cosmology. Companion papers derived an angular recording filter, a radial kernel, and a variance decoder from the `Participatory Modular Hamiltonian (PMH) '. The angular filter demonstrated it can resolve the low-power anomaly and the decoder reproduces the quadrupole--octopole alignment, but both channels record only unsigned threshold events and are provably parity-even. Here we show that all local recording-rate mechanisms are blocked from producing parity asymmetry by an exact spherical-harmonic identity, and that the rotationally covariant evasion within the present scalar pairing framework is a nonlocal antipodal kernel for which P_ (-1) = (-1) ^ preserves the parity sign. Three structural principles, namely the antipodal pairing map, the negative sign from evidence optimality, and a heat-kernel smoothing envelope, fix the form of the operator; a geometric scale closure then reduces the model to a single fitted parameter, the contrast amplitude~. The one-parameter model gives 2 = 5. 6 over CDM (² = -7. 4; = -3. 6). The geometric closure retains nearly the full likelihood of the freely fitted model, losing only (2) 0. 28 while reducing the fit from three parameters to one. The parity ratio anomaly moves from the 1--3\% tail to the 26--54\% bulk at every tested _, and the S₁/₂ resolution of the angular filter is preserved. The extended unified model is favoured over CDM by information criteria in its present construction. However, the contrast amplitude = 0. 27 remains a single fitted parameter. Resolving the programme's amplitude gap from first principles remains the framework's central open problem.