Time-Scalar Field Theory & Scalar-Time Cosmology: Unified Large-Scale Predictions and Multi-Domain Experimental Validation

We assemble a cosmology–to–laboratory validation of Time-Scalar Field Theory (TSFT) in which evolution occurs along a scalar-time potential Θ(x) with local rate α(x) > 0. A single continuity law ∇μ(αTμν) = 0 plus the unified evolution identity dO dΘ = α{O,H} (classical) or (i/ℏ)α[ ˆH ,O] (quantum) produces (i) an FRW-level modification that fits q(z) with one parameter, (ii) a weak-field exterior tail ∝ +k/r3 that accounts for perihelion precession and predicts Lagrange-point offsets and clock gradients, and (iii) laboratory-scale phase laws seen in modern interferometry. We perform a joint likelihood across four data families: cosmic expansion (q(z) bins), solar-system dynamics (Mercury precession; L1/L2 ephemerides, clock gradients), navigation/radio science (GPS, Cassini, MESSENGER/BepiColombo, Juno), and heliosphere edges (Voyager/IBEX/New Horizons). We close with targeted tests achievable with current assets.