The Participatory Decoder: Architecture for the Participatory Horizon Programme - Part III

Persistent large-angle anomalies in observational cosmology, including suppressed CMB correlations beyond $60^\circ$, excess source-count dipoles, and quadrupole--octopole alignment with the kinematic dipole and planarity (`Axis of Evil'), share an observer-dependent character that primordial mechanisms should not produce.  The participatory-horizon programme proposes that these anomalies arise because the observer's causal diamond acts as an information aperture whose geometry constrains which correlations are realised as classical records, while the standard $\Lambda$CDM cosmology is retained in full.  The companion PMH framework~\citep{OGradyPMH2026} derives an angular recording filter $h^2(\ell)$ and a radial kernel $k_L(x)$ from the conformal geometry of the causal diamond, and the companion Lindblad paper~\citep{OGradyLindblad2026} constructs the local irreversible recording dynamics with canonical collapse operator $\hat{R}_a = \delta\widehat{K}_a/\Sigma_W$.  Both papers identified a variance channel, $m$-dependent modulation from anisotropic position-space recording, but deferred its future quantitative development.

The central question addressed is whether position-space recording on the causal diamond can produce the observed quadrupole--octopole alignment and low-$\ell$ planarity, and if so, what the framework predicts for the pattern of $m$-dependent variance modulation in the low-$\ell$ CMB sky.

The framework yields exact, parameter-free variance coefficients, $\kappa_{20} = 2/7$, $\kappa_{21} = 1/7$, $\kappa_{22} = -2/7$, locked to the kinematic dipole direction.  The decoder concentrates Fisher information on zonal ($m = 0$) modes, suppressing their posterior variance while leaving sectoral ($|m| = \ell$) posterior variance relatively enhanced, thereby producing the geometry of the planar morphology observed in the CMB quadrupole.  A parity selection rule, following from the quadratic structure of the Lindblad hazard, forces the canonical decoder to be antipodally symmetric: it cannot produce a diagonal even/odd $C_\ell$ parity asymmetry.  A common-axis theorem shows that independent bias of the quadrupole and octopole axes toward $\hat{v}$ enhances their mutual alignment without requiring direct $\ell = 2 \leftrightarrow 3$ covariance coupling.

The amplitude falls short of the observational target by 15--17 orders of magnitude, and this gap is shown to be structural
within the canonical recording architecture.  The geometric predictions, i.e., the $\kappa_{\ell m}$ variance pattern, the parity selection rule, and the common-axis theorem, hold regardless of the amplitude and constitute parameter-free predictions of the framework.