Resolution of the Wide-Binary Gravity Anomaly via Unified Scalar Field Theory v3: A Parameter-Free External Field Effect

Gaia astrometry of wide binary stars has revealed a low-acceleration kinematic anomaly whose interpretation remains contested: analyses of statistically clean samples report an orbital-velocity boost ∼1.4× the Newtonian expectation at internal accelerations g ≲ 10−10 m s−2, while other groups working from the same catalogue find the data consistent with Newtonian gravity. We show that Unified Scalar Field Theory v3 (USFT v3) — a discrete tick-algebra framework whose only long-range gravitational object is the strictly linear scalar gravitational-tension field δG — predicts this anomaly with no free parameters, and in doing so resolves the apparent observational tension. Because δG obeys a linear Poisson equation and all forces route through the v3 N-body theorem, USFT v3 cannot generate an External Field Effect (EFE) through field nonlinearity as in AQUAL-type MOND; its EFE is instead a modified-inertia effect, arising from the tick-frequency crossover acting on the vector sum of internal and external baryonic accelerations. Fed the Milky Way external field aext = V02/R0 = 2.15×10−10 m s−2 (GRAVITY/Gaia Galactic constants) and the companion paper’s derived a0 = cH0/2π, the internal-gravity boost saturates at a plateau γ ≃ 1.3–1.4 rather than running to the isolated deep-MOND value √(a0/aint) ≃ 1.7. This plateau overlaps the reported ∼1.4 signal while remaining shallow enough to be masked in analyses with different orbit-deprojection priors, reconciling the two observational camps within a single theory. A 5×104-binary Monte Carlo forward model reproduces the analytic plateau and shows the isolated law is decisively excluded. We correct and supersede our own withdrawn 2026 preprint, which used the retracted quantum-decoherence a0 mechanism and the isolated deep-MOND scaling; both are shown here to be invalid for solar-neighborhood binaries.