Flow-Time Theory v6: Self-Consistent Field Theory of Entropy and Gravity

Flow-Time Theory v6: Self-Consistent Field Theory of Entropy and Gravity FTT v5 established a unified phenomenological framework from GPS to black holes, introducing the gravitational modulation function f(r) = (1 - r_s/r)/(1 - γ r_s/r) with γ ≈ 0.62, and the local cosmological curvature parameter R = 0.617 from GPS data. However, v5 left three open problems: (1) the exponent p = 3/2 in ∂_tΦ ∝ A(r)^p was selected by data rather than derived; (2) f(r) was constructed rather than solved from the field equation; (3) R was treated as a free parameter fitted to GPS data. This version (v6) closes these three gaps: (1) and (2) from first principles; (3) by recognizing R as a measured parameter. Starting from the Φ field action in Schwarzschild spacetime, we derive p = 3/2 from horizon regularity and the field equation, yielding D = 9ℓ_Pl². We then solve for f(r) from the radial equation with the source term (2φ_g/c²)∇²Φ₀, which emerges naturally from the linearized field equation. We show that R is a measured parameter (from GPS, v5) and that FTT requires no other free parameters. Furthermore, v6 provides a complete derivation of the emergence of macroscopic time from quantum decoherence via the self-environment of Φ field fluctuations, closing the "two times" gap left open in previous versions. The theory is now self-consistent, with all parameters except R derived from first principles. The value R = 0.617 is taken from GPS measurement (v5). The remaining predictions (U-axis direction, P1-U experiment, variation of R with position) are left for experimental test. P5 information retrieval (reported in v3, Cohen's d > 0.8, p < 0.001) provides direct empirical support for the information-field ontology of FTT, consistent with the Φ field encoding complete worldline information at temporal anchors. The gravitational entropy dynamics in v6 and the information encoding in P5 are two facets of the same underlying field: Φ.