The Participatory Horizon as an Angular Recording Filter: A Derived CMB Suppression Scale

The CDM model provides a thoroughly tested account of the cosmic microwave background, yet persistent anomalies at the largest angular scales remain unexplained. The most prominent is the low-power anomaly: the two-point correlation function effectively vanishes for separations 60^, with the observed S₁/₂ statistic falling below \, 99. 9\% of CDM realisations. The participatory horizon programme explores the hypothesis that such anomalies reflect the observer's finite causal domain acting as an information aperture on the recorded sky, retaining the standard cosmological background while encoding the horizon as a boundary condition on which correlations become irreversibly realised as classical records. An earlier paper in the programme fitted a phenomenological filter to Planck~TT bandpowers, but its functional form was ad~hoc and its cutoff scale was obtained from the data rather than predicted. Here we derive a replacement from three physical inputs: the angular Laplacian eigenvalue (+1) as the natural measure of modal complexity, the irreversibility of recording (Poisson statistics from independent absorbing events on the diamond boundary), and the conformal geometry of the observer's causal horizon. The result is an exponential saturation filter, h² () = 1 - - (+1) /₂^\, 2, whose transition scale ₂^\, 2 is predicted from the ratio of the conformal time to the comoving distance to last scattering. The geometric prediction ₂^\, 2=12. 6--13. 0 matches the value preferred by Planck~TT bandpowers (₂^\, 2=9. 5 5. 2 from an f ₒ₊ₘ-corrected scaled-² likelihood) to within 1 (0. 59). The derived filter suppresses =2--7 smoothly rather than concentrating at the quadrupole alone. A 10, 000-realisation bandpower-based Monte Carlo shows that the filter transforms S₁/₂ from anomalous (8th percentile of CDM) to typical (32nd percentile of the filtered model). Under the simplest universality assumption, the same filter suppresses the reionisation bump in the EE spectrum at =2 by \, 53\% with zero additional parameters. Falsification tests, limitations, and implications are discussed.