Lensing Amplitude Bias (A_lens=1.18)

The lensing amplitude parameter A_lens characterizes the degree to which the CMB power spectrum has been smeared by gravitational lensing along the line of sight. Planck data consistently prefer A_lens ≈ 1.18, meaning the CMB appears more lensed than ΛCDM predicts — an excess at ~2.8σ. In a standard single-frame cosmology, all lensing deflection comes from discrete mass concentrations along each photon path, and the total lensing power is calculable from the matter power spectrum. Successive Collision Theory adds an additional source of lensing power that is absent from ΛCDM: the coherent gravitational superposition of overlapping nested comoving frames along the line of sight. When photons traverse the boundaries of overlapping frames on their journey from the last scattering surface, they experience the superposed gravitational field of multiple frame hierarchies simultaneously. This constructive gravitational superposition deflects CMB photons beyond what discrete particle-counting would predict, increasing the effective lensing amplitude above unity without requiring any additional matter.

The magnitude of the A_lens excess directly constrains the depth of the gravitational superposition along a typical line of sight to the CMB. The inferred value of A_lens ≈ 1.18 corresponds to an ~18% excess in lensing power — a quantity that SCT predicts should scale with the number density and characteristic depth of the frame boundaries intersected along the ~14 Gpc path length to the last scattering surface. This is not a free parameter but a prediction tied to the same superposition amplitude that explains flat galaxy rotation curves and the S8 tension on different scales. The fact that A_lens > 1 is found independently from the same Planck dataset that constrains S8 and Ω_K provides a self-consistent picture: all three anomalies point toward a gravitational influence above the ΛCDM expectation, and all three find a common explanation in the coherent superposition of nested comoving frames that SCT's collision scenario naturally produces.