Domain of Validity and Quantum Transport in the Guerrero si-FDM Framework: Full Rotation Curve Analysis of SPARC-174 and the Relaxation Timescale Criterion

We present the full rotation curve analysis of 174 galaxies from the SPARC catalog within the Guerrero self-interacting fuzzy dark matter (si-FDM) framework (m22 = 8.0, g_NL = 0.00597, r_c = 1.5 kpc), extending the asymptotic V_flat baseline established in Paper 6 (zenodo.20219427). By implementing a point-by-point fitting pipeline using 3,391 data points with baryonic decomposition and a Bayesian prior on stellar mass-to-light ratios (Upsilon_disk), we show that the global 18.4% success rate conflates two physically distinct populations. We formalize the extension of the Guerrero EFT into a quantum transport theory by deriving the complete quantum stress-momentum tensor (Π_ij^Bohm) via the Madelung hydrodynamics representation, which yields a universal r^(-2) correction to circular velocities relevant below r_Q ~ 0.6 kpc. Furthermore, we derive an analytic quantum relaxation timescale from first principles that scales as τ_relax ∝ M_h^(7/3). The condition τ_relax = t_Hubble defines a critical flat velocity threshold V_crit ≈ 100 km/s. Statistical validation via the Mann-Whitney test confirms (p < 0.0001) that halos below V_crit have reached their stable solitonic ground state (achieving a 58% success rate), while massive halos (V_flat > 100 km/s) remain outside the equilibrium domain. Finally, we introduce the inverse core contraction hypothesis for massive galaxies (M_h > 10^11.5 M_sun), where CMB-excited condensates undergo quantum evaporation and core mass loss over cosmic time, establishing a discriminating, zero-free-parameter prediction to be developed in Paper 8.