Temporal Equivalence Principle: Synchronization Holonomy in Pulsar Scintillation

Standard scintillation theory treats each scattered ray as carrying a scalar delay, so differential delays around a closed triplet cancel identically: tau_ij + tau_jk + tau_ki = 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 psi_bar = 0.984 ± 0.046 rad with R_bar = 0.308; the directional V-test shows significant directional concentration relative to the pre-specified null direction mu_0 = 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 H_trim = 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.