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We formulate a scalar-tensor theory in the physical frame, where the fundamental scalar variable is the local temporal flow rate τ(x) = e^{σ(x)} > 0, coupled to a fractal texture tower {Φ_n} with geometric mass hierarchy q^{-2n} (q = √2). The physical-frame action features a non-constant scalar kinetic factor K(σ) = 6 − αe^{-2σ}, a stabilized temporal potential U₀(σ) = Λ₀e^{-λσ} + Λ_b e^{νσ} (with λ = 4 − p, creating a hard wall as τ → 0), and texture fields that are non-canonically normalized in the physical frame due to the conformal transformation. Rigorous results: Exact local GR branch: when σ = σ* (stable minimum), the field equations reduce exactly to Einstein + Λ_eff, giving Schwarzschild–de Sitter. Singularity avoidance: the temporal potential U₀ diverges at both σ → −∞ (τ → 0) and σ → +∞, confining the system. Kinetic health: K(σ) > 0 for τ > 1/√3 with α = 2; explicit parameter condition ensures the stabilized branch is healthy. Dark energy: frozen light texture modes (n > n*) provide w_DE ≈ −1 near the stabilized branch. Gravitational waves propagate at c exactly on the stabilized branch. Compatibility result (not a full theorem): The temporal profile τ(r) = √(1 − r_s/r) satisfies □̃(ln τ) = 0 on a fixed Schwarzschild background. A full proof that the coupled field equations admit exact Schwarzschild globally remains open. Structural choices (not derived theorems): The package (α, p, q) = (2, √2, √2) is retained as a closure hypothesis. The theory is not standard Brans-Dicke with constant ω_BD; standard BD formulas do not apply. Version 4 — complete rewrite in a single physical frame, resolving the mixed-frame issues of earlier versions.