Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars

Gravitational time dilation in General Relativity is verified to 10−5 precision in the Solar System. At intermediate astrophysical scales, however, persistent anomalies emerge—rotation curves, cluster dynamics, cosmic acceleration—that conventionally require invisible matter or exotic energy. The Temporal Equivalence Principle (TEP) formalizes an alternative: that time dilation is scale-dependent, enhanced in extended gravitational configurations while screened in dense, well-tested regimes. This work reports a dynamical anomaly in globular cluster pulsar timing that challenges standard density scaling. Pulsar timing provides a spatially-resolved probe of time-dilation effects at the 10⁵–10⁶ M☉ scale. Analysis of 543 millisecond pulsars (197 GC, 346 field) reveals a 0.63 dex (decimal exponent, factor of ~4.3) raw excess in spin-down magnitude—cluster pulsars spin down faster than field controls. After controlling for population differences, a 0.40 dex controlled residual persists (95% CI: 0.33–0.48 dex, 8.3σ). A spatially-stratified spin-down anomaly is detected in 197 globular cluster pulsars compared to 346 field controls (0.63 dex raw excess, 0.40 dex controlled residual, 8.3σ from covariance-aware test). The signal exhibits suppressed density scaling (mixed-effects slope Γ = 0.39 ± 0.08 dex/dex vs Newtonian ensemble baseline Γ = 0.72; 4.1σ rejection, Bayesian P(Γ > 0.72|data) < 10⁻⁴), saturating in dense cores in a manner consistent with TEP screening but in tension with standard dynamics. Leave-one-cluster-out validation confirms the result is stable (3.8% relative instability) and not driven by individual clusters. A "Binary Inversion" is detected where typically noisy binary systems—predicted to be dynamically hotter—exhibit significantly lower residuals (-0.32 dex, Mann-Whitney p=0.004) than isolated pulsars, challenging standard dynamical heating models. Together, the raw excess, controlled residual, and suppressed density scaling argue against standard Newtonian dynamics as a complete explanation. The pulsar signal—spatially resolved, field-controlled, and showing suppressed density scaling—provides the primary evidence for potential-dependent modifications to gravitational time flow. Website: https://mlsmawfield.com/tep/cos/Code Availability: https://github.com/matthewsmawfield/TEP-COS DOI: 10.5281/zenodo.18165798 Keywords: temporal equivalence principle – pulsar timing – globular clusters – time dilation – screening transition – modified gravity 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.