Processing Proxies II: Aird-Anchored Accretion Coupling and the Kernel-II Sigma-Response Constraint

This version revises the framing of Processing Proxies II while preserving the numerical core of the original calculation. The paper connects the multichannel source logic of Processing Proxies I with the Kernel-Cosmology II sigma response variable by testing whether a phenomenological accretion-like source history can drive the response toward the Kernel-II reference neighborhood near sigma_* = 2/3.

The source curve used here is a normalized accretion-like profile motivated by the broad redshift behavior of AGN/X-ray luminosity-function studies, but it is not a direct digitization of Aird et al. The constrained quantity is therefore the normalized effective coupling A_eff = A s, with s_ref defined by max Sigma_dyn = 1, rather than a microscopic coupling derived from first principles.

The revised version adds a more conservative interpretation of the result, reports tolerance sensitivity around sigma_* at ±5%, ±10%, and ±20%, includes useful-window clipping of the near-star amplitude intervals, clarifies initial-condition robustness, and emphasizes that the linear scaling in A applies only to the decoupled sigma-response test. No claim of observational confirmation is made.

The result should be read as a falsifiable normalized response constraint: an accretion-like temporal source shape can drive the Kernel-II sigma response into the fixed-point neighborhood if the effective normalization is of order unity, while a fully data-calibrated accretion reconstruction and a coupled Kernel-II stability test remain tasks for future work.