Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries

The Gaia DR3 catalog of over one million wide binaries opens 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 v0. 8 Jakarta) —in which a conformal scalar field modulates matter proper time as dτ/dt ≈ A (φ) (with A (φ) = exp (βφ/MPl) ) with the Cepheid-calibrated response scale denoted κCep, while the wide-binary transition is parameterized independently by the velocity-profile saturation amplitude αₛat, not by a bare scalar coupling—addresses that tension through smooth Temporal Shear recovery in weak-field environments. This paper tests whether the Gaia wide-binary anomaly is better described as smooth Temporal Shear recovery in weak-field environments. From 341, 315 high-purity systems, the analysis identifies a screening transition at Rₛ = 2, 646 ± 182 AU (statistical; ± 609 AU total), strongly preferred over both a flat Newtonian profile (Δχ² = 14, 845) and a constant boost (Δχ² = 3, 583). At large separation the profile saturates at αₛat = 0. 366 ± 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. With a non-circular metallicity guardrail that uses a conservative external βMLR prior unless independent spectroscopic metallicities are cached, the lower-density high-|Z| population transitions at smaller radius than the higher-density midplane (Rₛ = 4, 662 ± 196 versus 7, 131 ± 1, 341 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 and phase-mixed Newtonian orbital forward models fail to reproduce the observed screening preference. 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 environmental ordering are quantitatively consistent with the conformal scalar field of TEP and are not reproduced by the Newtonian orbital-projection or MOND/EFE parameterizations tested here. Website: https: //mlsmawfield. com/tep/wb/Code Availability: https: //github. com/matthewsmawfield/TEP-WB DOI: 10. 5281/zenodo. 19102061 Keywords: Temporal Equivalence Principle – wide binaries – Gaia DR3 – weak-field gravity – Temporal Shear recovery – environmental transition morphology – Temporal Topology – Temporal Shear – modified gravity – MOND Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All materials required for full reproducibility—including data downloads, analysis scripts, code, and manuscripts—are open-source. Feedback and contributions to further test these results are welcome.