QHCC Practical Note II: Testing the FLiC Echo Formula in NGC 5548 Accretion Lags

This technical note presents an accretion-side test of the QHCC/FLiC echo-delay formula using multiwavelength reverberation data of NGC 5548. The tested observer-frame delay is Δt_obs(M; α, z) = (1 + z) α (r_S / c) ln(r_S / ℓ_P), where r_S = 2GM/c² is the Schwarzschild radius, ℓ_P is the Planck length, z is the redshift, and α defines the FLiC branch. The two tested branches are α = 2/3 for the one-way FLiC echo and α = 4/3 for the two-way FLiC echo. For NGC 5548, using an independently adopted black-hole mass M = 6.5 × 10⁷ M☉ and redshift z = 0.017175, the formula predicts observer-frame delays of 12.796 hours for the one-way branch and 25.593 hours for the two-way branch. The analysis compares these fixed, non-fitted delay scales with the observed lag–wavelength structure across ultraviolet and optical bands. The main result is a FLiC-dominated accretion lag layer: selected one-way lag peaks form a low-jitter structure around the fixed 12.8-hour scale, while the cleanest two-way optical point lies close to the predicted 25.6-hour scale. The note further compares this morphology with pure disk-only lag models and finds that the observed lag–wavelength structure is better described as a fixed FLiC delay plus a small wavelength-dependent disk correction than as a purely disk-driven reverberation curve. This work should be read as a candidate-level observational validation of the FLiC echo formula in accretion data, complementary to the binary black-hole gravitational-wave analysis presented in Practical Note I.