Flow-Time Theory: Self-Consistent Field Theory of Entropy and Gravity - Version 6.1

This paper presents the self-consistent field theory formulation of Flow-Time Theory (FTT) v6.1, in which time, space, and gravity are not fundamental but emerge from a scalar field Φ and its gradient ∇ρ. The core entropy production rate is dS/dλ = k|∇ρ|·sgn(ρ). The theory derives from first principles: (1) the exponent p = 3/2 in ∂_tΦ ∝ A(r)^p, yielding D = 9ℓ_Pl²; (2) the unified gravitational modulation function f(r) = (1 - r_s/r)/(1 - R r_s/r) with R ≈ 0.617; (3) the emergence of macroscopic time from quantum decoherence of the Φ field itself. The GPS gravitational time offset (Δf/f = 5.2×10⁻¹⁰) is matched using R measured from GPS data, not fitted. This version (v6.1) corrects an algebraic typo in Section 6 (GPS derivation) present in v5/v6. The correct relation is α = (2/c²)·(1-R). Consequently, 1-R = α_obs/(2/c²) = 0.383 and R = 0.617. All physical content, numerical values, and experimental predictions remain unchanged. See Appendix F for details. Keywords: Flow-Time Theory, entropy gradient, Φ field, GPS time dilation, emergent time, quantum decoherence, P5 information retrieval.