The 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 394 millisecond pulsars (196 GC, 198 field) reveals a 0. 61 dex raw excess in spin-down magnitude—cluster pulsars spin down faster than field controls. After controlling for population differences, a 0. 58 dex residual persists (95% CI: 0. 52–0. 63 dex, 5. 8σ–7. 7σ depending on correlation treatment). A spatially-stratified spin-down anomaly is detected in 196 globular cluster pulsars compared to 198 field controls (0. 61 dex raw excess, 0. 58 dex controlled residual, 5. 8σ from covariance-aware test). The signal exhibits suppressed density scaling (mixed-effects slope Γ = 0. 39 ± 0. 08 dex/dex vs Newtonian Γ = 0. 72; 4. 1σ rejection, Bayesian P (Γ > 0. 72|data) = 4×10⁻⁵), 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, p=0. 007) than isolated pulsars, challenging standard dynamical heating models. Cluster Monte Carlo (CMC) comparison using 13 clusters (M62, M15, M13, Terzan 5, NGC 6517, 47 Tuc, M28, M3, M4, M5, Omega Cen, NGC 6397, NGC 6752) and 21. 0 million synthetic pulsars tests standard dynamical explanations. CMC predicts 2. 10 dex raw excess (3. 1× larger than observed, 13. 1σ prediction mismatch) and density scaling slope 0. 75 (4. 0σ discrepancy from observed 0. 39). Standard Newtonian dynamics cannot reproduce the observations; standard dynamics is disfavored. Complementary analysis of Type Ia supernovae (N=218) reveals a correlation between peak magnitude and host velocity dispersion consistent with TEP time dilation predictions, exhibiting a 3. 24σ Pearson correlation with structure near σ ≈ 165 km/s. Note: This signal is indistinguishable from the standard mass-step effect; presented as exploratory support only. The convergence of time-domain evidence (pulsars) with N-body dynamics validation (CMC) presents a coherent "Ladder of Evidence" for potential-dependent modifications to gravitational time flow. The pulsar signal is spatially resolved, field-controlled, and shows suppressed density scaling consistent with the saturation of a gravitational soliton at the screening transition scale predicted by the universal critical density ρc ≈ 20 g/cm³. Website: https: //mlsmawfield. com/tep/cos/Code Availability: https: //github. com/matthewsmawfield/TEP-COS This work is a preprint and is open to community review and collaboration. All analysis code, data, and manuscripts are open-source and available at https: //github. com/matthewsmawfield/TEP-COS. Feedback and contributions to further test these results are welcome. Keywords: temporal equivalence principle, pulsar timing, globular clusters, gravitational lensing, time dilation, screening transition, modified gravity