Fixed Inner Quantum-Horizon Echo Branches in O4a Binary Black-Hole Data

This technical note presents a random-sample O4a binary black-hole validation of a fixed inner quantum-horizon echo-delay law. The analysis tests the fixed physical branches $\alpha = 2/3$ and $\alpha = 4/3$ across component-mass channels, using a reproducible random sample of 30 posterior-eligible events selected from a pool of 77 O4a events with a fixed seed. The methodology relies on 32-second event-centred strain windows, 5000-null trial calibrations, and non-physical control branches without fitting the delay to the strain data. The physical branches produce clean, two-detector, sign-coherent scale compatibility in 26 out of 30 randomly selected events, yielding an event-level Fisher probability of $4.59 \times 10^{-23}$. The physical predictions substantially outperform all tested non-physical control branches in event count, clean-row count, and combined significance, supporting the interpretation that the observed echo-candidate structure is preferentially organised by the fixed logarithmic mass-scaled delay law. The note includes the methodological description, random-sample selection criteria, 5000-null calibration statistics, control-branch comparisons, and details for a frozen pre-O4b replication path to ensure strict forward-testing on upcoming data. Reproducibility references and links to the frozen codebase are provided.