Temporal Equivalence Principle: Temporal Shear in the Earth Flyby Anomaly

Twelve Earth gravity assist flybys spanning nine spacecraft are analyzed within the Temporal Equivalence Principle (TEP) framework. TEP posits that global simultaneity is inherently non-integrable, with the rate of time represented as a dynamical scalar field φ. All non-gravitational matter couples universally to a causal matter metric through conformal coupling A(φ) = exp(β φ/M_Pl), producing a scalar force F = β_eff c² ∇φ/M_Pl on test masses, where β_eff = β × S_⊕(r) incorporates geometric screening via Temporal Topology. The screening factor S_⊕(r) encodes continuous suppression of Temporal Shear in density gradients, with a characteristic transition radius R_sol ≈ 4146 km derived from the UCD saturation model and independently validated by GNSS atomic clock correlations (λ_TEP ≈ 4000 km). The scalar force manifests as a "Phantom Mass" artifact — velocity anomalies that mimic unmodeled gravitational mass distributions. The non-radial component, modulated by Earth's oblateness (J2, J3, J4), trajectory asymmetry, velocity-dependent disformal coupling, and perigee plasma environment, produces the observed flyby anomaly. Four published anomalies are retained in the catalog (NEAR, Galileo 1990, Rosetta 2005, Cassini), alongside five published nulls/bounds and three flybys without public anomaly reports. Information-criterion comparisons on the full catalog of nine flybys with published observations (n = 9) favour the TEP restricted model under the adopted full-catalog likelihood over both the Null (ΔBIC ≈ 714) and the Anderson empirical baseline (ΔBIC ≈ 79), using a single fitted parameter β with λ_TEP, S_⊕, and v_trans pre-specified from independent data and first-principles derivations. The magnitude of this separation depends on the treatment of systematic uncertainty (a geometry-spread σ_geom ≈ 1.20 mm/s is adopted because the tiny published per-flyby uncertainties would otherwise produce astronomically large, scientifically meaningless values) and should be interpreted as model-selection support rather than calibrated evidence. The gated n = 3 subset yields weaker TEP-restricted vs Anderson separation (ΔBIC ≈ 19), confirming that the null flybys are essential for discriminating the physics-based model from the empirical baseline. The random-effects summary β_RE ≈ 2.56 × 10⁻³ ± 7.85 × 10⁻⁴ (SE; between-flyby τ ≈ 1.49 × 10⁻³) quantifies the honest cross-flyby amplitude scale, while the per-flyby fits span 1.01 × 10⁻³ to 5.33 × 10⁻³ consistent with geometry-dependent modulation. All fitted amplitudes satisfy PPN constraints via Temporal Topology screening (|γ − 1| ≈ 2β_eff² < 2.3 × 10⁻⁵). Cassini's small predicted anomaly in the mixed disformal regime, where conformal-gradient and disformal terms partially cancel at the reference coupling, is consistent with the velocity-dependent regime structure predicted by the TEP field equations (v_trans ≈ 16.8 km/s), though the literature geometry sign remains an open diagnostic stress test rather than a resolved confirmation. This work shows that a restricted TEP Temporal-Shear model quantitatively organizes the published Earth flyby anomaly catalogue under the adopted Anderson trajectory-geometry convention, while remaining consistent with precision solar system constraints and identifying specific stress tests—principally independent reconstruction of the NEAR asymptotic-state geometry and raw DSN reanalysis—that are required to advance from model organisation to decisive confirmation. Website: https://mlsmawfield.com/tep/efa/Code Availability: https://github.com/matthewsmawfield/TEP-EFA DOI: 10.5281/zenodo.19454863 Keywords: Earth flyby anomaly, Temporal Equivalence Principle, scalar force, Phantom Mass, trajectory asymmetry, geometric screening, Temporal Topology, Temporal Shear 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.