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, gNL = 0. 00597, rc = 1. 5 kpc), extending the asymptotic Vflat 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 (Upsilondisk), 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 (ᵢjBohm) via the Madelung hydrodynamics representation, which yields a universal r^ (-2) correction to circular velocities relevant below rQ ~ 0. 6 kpc. Furthermore, we derive an analytic quantum relaxation timescale from first principles that scales as ᵣelax Mₕ^ (7/3). The condition ᵣelax = tHubble defines a critical flat velocity threshold Vcrit 100 km/s. Statistical validation via the Mann-Whitney test confirms (p 100 km/s) remain outside the equilibrium domain. Finally, we introduce the inverse core contraction hypothesis for massive galaxies (Mₕ > 10¹1. 5 Mₛun), 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.