Practical Note IX: Network-Coherent Echo-Mass Recovery in O4b Binary Black-Hole Strain Data

This practical note presents a reduced-strain O4b test of the fixed-branch QHCC echo-mass estimator for binary black-hole events. The analysis uses the two predicted echo-delay branches, $α = 2/3$ and $α = 4/3$, applies a network-aware detector classification to public O4b strain data, and inverts the observed echo delays into component echo masses. In the O4b rerun, 27 events containing 54 progenitor black-hole components are analyzed. The estimator recovers catalog-compatible echo masses for 31 out of 54 components in the scale-compatible layer, including 9 strict peff <= 0.05 component recoveries and 10 two-branch mass-consistency cases. The median mismatch between the recovered echo masses and the catalog component masses is approximately 4%. To test whether this agreement could arise from accidental catalog-mass assignment, 50,000 empirical null trials were performed using both component-shuffle and event-pair-shuffle ensembles. The observed mass-recovery counts are not reproduced by the randomized nulls. The resulting conservative empirical mass-recovery bound is pₘₐₛₛ ≤ 4.0 × 10⁻⁵. The result does not constitute a standalone global detection statistic. Rather, it establishes a reproducible mass-consistency layer: fixed QHCC echo-delay rows, measured in public O4b strain data, return catalog-compatible component masses significantly more often than expected under randomized mass assignments. Python scripts for reproducing the analysis are provided in the accompanying GitHub repository.