Standard scintillation theory treats each scattered ray as carrying a scalar delay, so differential delays around a closed triplet cancel identically: tauᵢj + tauⱼk + tauₖi = 0. The Temporal Equivalence Principle (TEP) instead predicts that proper-time transport is path-dependent in low-density, unscreened environments, producing a non-zero synchronization holonomy. This paper reports the rejection of the scalar-delay null hypothesis in pulsar scintillation using the phase-domain closure statistic psi, a zero-centered circular observable that separates geometric phase from folded-noise bias. The primary target is PSR J0437-4715, analyzed with 19, 167 scintillation triplets from 1, 391 closure-capable Parkes/PPTA epochs; 1, 093 epochs form the independent sample. The broader 15-pulsar catalog includes PSR J1603-7202, ten Jiamusi pulsars, and three MeerKAT pulsars. While J0437-4715 provides the primary phase-domain rejection of the psi = 0 null, PSR J1603-7202 contributes complementary bipolar geometric structure from a distinct line of sight at different velocity geometry. Furthermore, the distant Jiamusi and MeerKAT samples are noise-limited, consistent with TEP's predicted environmental suppression in dense environments. J0437-4715 shows a non-zero Phase Closure signal. The weighted circular mean is psibar = 0. 984 ± 0. 046 rad with Rbar = 0. 308; the directional V-test shows significant directional concentration relative to the pre-specified null direction mu₀ = 0 at p = 2. 04 × 10^-5, and the 95% bootstrap confidence interval 0. 737, 1. 235 rad excludes zero. The distribution is non-uniform (Rayleigh p = 1. 34 × 10^-44), identical in heliocentric and CMB-frame analyses, confirming that the rejection is not a frame-dependent artifact. PSR J1603-7202 has a 73. 8° proper-motion separation from J0437-4715 and exhibits a frame-independent bipolar geometric structure, matching TEP predictions for high-dispersion sightlines where the monopole is washed out. The Jiamusi and MeerKAT samples are consistent with the expected environmental suppression at large distances. The raw unsigned delay magnitude for J0437-4715, |H| = 8. 100 ± 0. 102 ns, operates at the expected folded-normal noise floor E|H| = 6. 810 ns (see Section 2. 1. 1). A robust trimmed amplitude Hₜrim = 21. 991 ± 0. 483 ns (45. 5σ) serves as a secondary robustness diagnostic; it does not carry primary inferential weight. Multiple independent checks support the phase-domain result. Phase-scramble and pre-alignment controls pass, unweighted psi is strictly frame-invariant, signed-delay cancellation behaves as expected for a bipolar signal, and rigorous synthetic noise tests confirm zero false positives. A signed-delay orbital diagnostic shows phase-locked structure directionally consistent with TEP kinematic coupling, though the hierarchical mixed-effects amplitude is not independently significant (p = 0. 372, 2 df), as expected for a partially screened orbital channel. Multi-pulsar scaling, chromaticity, cross-telescope environmental bounds, and orbital structure provide multiscale consistency checks on the TEP framework. The principal empirical result is the detection of non-zero Phase Closure on the J0437 sightline. Standard scalar-delay ISM models—including thin-screen Kolmogorov, multi-screen, refractive wandering, chromatic plasma, and Doppler-delay covariance models—predict psi = 0 and are rejected by this observation. The geometric structure from J1603-7202 and the environmental-suppression consistency in the distant pulsars are directionally consistent with the Temporal Equivalence Principle's non-integrable time transport. Website: https: //mlsmawfield. com/tep/j0437Code Availability: https: //github. com/matthewsmawfield/TEP-J0437 DOI: 10. 5281/zenodo. 19454620 Keywords: Temporal Equivalence Principle, pulsar scintillation, synchronization holonomy, closure delays, modified gravity, interstellar medium, multi-pulsar analysis, PSR J0437-4715, PSR J1603-7202, arc curvature scaling, scattering strength 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.
Matthew Lukin Smawfield (Sun,) studied this question.