The $\Lambda$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 $\ell \lesssim 30$. This programme hypothesises that such anomalies reflect the observer's causal diamond acting as a recording aperture on the observed sky, while retaining $\Lambda$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 $P_\ell(-1) = (-1)^\ell$ 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~$\rho$. The one-parameter model gives $2\Delta\ln\mathcal{L} = 5.6$ over $\Lambda$CDM ($\Delta\chi^2 = -7.4$; $\Delta\mathrm{AIC} = -3.6$). The geometric closure retains nearly the full likelihood of the freely fitted model, losing only $\Delta(2\ln\mathcal{L})\simeq0.28$ 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 $\ell_{\max}$, and the $S_{1/2}$ resolution of the angular filter is preserved. The extended unified model is favoured over $\Lambda$CDM by information criteria in its present construction. However, the contrast amplitude $\rho = 0.27$ remains a single fitted parameter. Resolving the programme's amplitude gap from first principles remains the framework's central open problem.