Temporal Equivalence Principle: Density-Dependent Screening in Gaia DR3 Wide Binaries

The Gaia DR3 catalog of over one million wide binaries provides a precise window onto gravity in the weak-field regime (a ≲ 10⁻¹⁰ m/s²), yet whether the observed velocity excess reflects modified gravity or unresolved systematics remains contested. This paper shows that the Temporal Equivalence Principle (TEP) —in which a conformal scalar field modulates matter proper time as dτ/dt ≈ A (φ) ¹/²—addresses that tension through density-dependent screening. From a high-purity subset of 341, 315 systems, the analysis identifies a screening transition at Rs = 2, 461 ± 178 AU (statistical; ± 638 AU total), strongly preferred over both a flat Newtonian profile (Δχ² = 16, 269) and a constant boost (Δχ² = 3, 756). At large separation the profile saturates at αₛat = 0. 380 ± 0. 012, roughly 35–40% above the Keplerian baseline. Broader smooth-transition fits preserve the same few-thousand-AU onset. The signal also shows the environmental ordering required by TEP. After metallicity-dependent mass corrections and bootstrap uncertainty estimation, the lower-density high-|Z| population transitions at smaller radius than the higher-density midplane (Rs = 3, 984 ± 192 versus 6, 881 ± 1, 267 AU), confirmed by a solar-track control (Rs = 4, 145 ± 276 versus 6, 856 ± 920 AU; permutation p < 10⁻⁴ for the full sample and p < 10⁻³ for the solar track). Scrambling tests fail to reproduce the observed screening preference (p < 10⁻⁴). The wide-binary anomaly is therefore not a generic low-acceleration excess but a structured, environmentally modulated screening transition—one whose morphology, onset scale, and density dependence are quantitatively consistent with the conformal scalar field of TEP and are not reproduced by MOND with or without the External Field Effect. Website: https: //mlsmawfield. com/tep/wb/Code Availability: https: //github. com/matthewsmawfield/TEP-WB Keywords: Temporal Equivalence Principle – wide binaries – Gaia DR3 – weak-field gravity – density-dependent screening – chameleon gravity – Temporal Topology – Temporal Shear – modified gravity – MOND