Practical Note IV: Testing a Mass-Scaled Quantum-Horizon Echo in NGC 4151 Accretion Lags

This practical note tests a fixed mass-scaled quantum-horizon echo-delay law in the public Swift multiwavelength monitoring data of NGC 4151. The tested delay is not fitted to the lag data. It is computed from the black-hole mass and redshift using the two fixed branches Δ tobs(M;α,z)=(1+z)S(M)/cS(M)/P, where rS(M)=2GM/c² and the physical branch coefficients are α=2/3 and α=4/3. The physical origin of the two branches is the two-screen black-hole relation Rqh³=rSP², which gives the one-way branch Δ t1w 2/3rS/cS/P and the two-way branch Δ t2w 4/3rS/cS/P. For NGC 4151, using M_•=4.57×10⁷ M_ and $z=0.003262$, the predicted observer-frame delays are Δ t1w,obs=8.844\ h and Δ t2w,obs=17.689\ h. The UV/optical lag-wavelength structure shows two near-horizontal lag layers close to these fixed predictions. The selected one-way layer has mean lag Δ t1w=9.336\ h, and the selected two-way layer has mean lag Δ t2w=18.480\ h. Their observed ratio is 18.480/9.336=1.979, close to the predicted two-branch ratio of $2$. Inverting the same fixed delay law gives timing-mass estimates of approximately Mecho,1w4.82×10⁷ M_ and Mecho,2w4.77×10⁷ M_, consistent with the adopted reverberation-mapping mass scale of NGC 4151. The note compares the fixed quantum-horizon delay layers with disk-only lag-wavelength curves. A pure disk-only no-offset model does not naturally reproduce the two near-horizontal layers, while an offset-dominated disk-plus-offset fit effectively behaves as a common-delay model. The main result is therefore not a single lag coincidence, but a two-branch timing structure: the same response channels show both the one-way and two-way predicted delay layers. This record includes the PDF technical note, figures, selected lag-layer tables, model-comparison outputs, and reproducibility materials used to generate the reported NGC 4151 result.