Practical Note V: Mrk 509 as a Mass-Prior-Constrained Two-Branch Quantum-Horizon Echo Candidate

This practical data-analysis note applies the Paper-I mass-scaled quantum-horizon delay law to public Swift UV/optical monitoring data for the active galaxy Mrk 509. The analysis treats the black-hole mass as a broad external nuisance parameter and scans a mass grid from $1.0\times10^8$ to $3.0\times10^8,M_\odot$, while keeping the physical branch coefficients fixed at $\alpha=2/3$ and $\alpha=4/3$. The best physical two-branch solution occurs near $M=2.72\times10^8,M_\odot$. At this mass, the predicted observer-frame delays are $55.19$ h and $110.38$ h, while the selected Swift UV/optical response-band lag peaks form two nearly horizontal common-delay layers centred at $55.80$ h and $110.88$ h. The observed layer ratio is $1.987$, close to the expected factor of two between the two branches. Inverting the same delay law gives echo-mass estimates of $2.750\times10^8,M_\odot$ and $2.732\times10^8,M_\odot$, showing sub-percent agreement between the two branch-derived timing masses. The result is classified as a strong QHCC-compatible double-lag candidate and as a demonstration of the two-branch delay law as a possible timing-mass estimator. It is not presented as a standalone proof of the normalization, because broad mass uncertainty allows ratio-2 control branch pairs to partially rescale the same absolute lag structure at different masses. The note therefore identifies Mrk 509 as a high-priority target for literature-mass-prior refinement, wrong-ratio controls, trials-aware significance estimates, and multi-object AGN population validation.