Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars

Author: Matthew Lukin Smawfield
Version: v0.5 (Caracas)
Date: First published: 9 January 2026 | Updated: 24 April 2026
Status: Preprint
DOI: 10.5281/zenodo.18165798
Website: https://mlsmawfield.com/tep/cos/
Paper Series: TEP Series: Paper 10 (Cosmological Observations)

Abstract

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 0.59 dex (decimal exponent, factor of ~3.9) raw excess in spin-down magnitude—cluster pulsars spin down faster than field controls. After controlling for population differences, a 0.61 dex residual persists (95% CI: 0.55–0.66 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 (0.59 dex raw excess, 0.61 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 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.

Key Findings

Analysis of 394 millisecond pulsars reveals a 5.8σ dynamical anomaly (5.8σ from covariance-aware test, 7.7σ from Welch t-test): globular cluster pulsars spin down 0.59 dex (raw) to 0.61 dex (controlled) faster than field controls. The density scaling is suppressed (slope Γ = 0.39 ± 0.08 vs Newtonian ensemble baseline Γ = 0.72; 4.1σ rejection), and binary pulsars in clusters are unexpectedly quieter than isolated pulsars (−0.32 dex, Mann-Whitney p = 0.004)—challenging standard dynamical heating models. Leave-one-cluster-out validation confirms the result is stable (3.8% relative instability).

---

The TEP Research Program

Paper	Repository	Title	DOI
Paper 0	TEP	Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed	10.5281/zenodo.16921911
Paper 1	TEP-GNSS	Global Time Echoes: Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17127229
Paper 2	TEP-GNSS-II	Global Time Echoes: 25-Year Temporal Evolution of Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17517141
Paper 3	TEP-GNSS-RINEX	Global Time Echoes: Raw RINEX Validation of Distance-Structured Correlations in GNSS Clocks	10.5281/zenodo.17860166
Paper 4	TEP-GL	Temporal-Spatial Coupling in Gravitational Lensing: A Reinterpretation of Dark Matter Observations	10.5281/zenodo.17982540
Paper 5	TEP-GTE	Global Time Echoes: Empirical Validation of the Temporal Equivalence Principle	10.5281/zenodo.18004832
Paper 6	TEP-UCD	Universal Critical Density: Unifying Atomic, Galactic, and Compact Object Scales	10.5281/zenodo.18064366
Paper 7	TEP-RBH	The Soliton Wake: A Runaway Black Hole as a Gravitational Soliton	10.5281/zenodo.18059251
Paper 8	TEP-SLR	Global Time Echoes: Optical Validation of the Temporal Equivalence Principle via Satellite Laser Ranging	10.5281/zenodo.18064582
Paper 9	TEP-EXP	What Do Precision Tests of General Relativity Actually Measure?	10.5281/zenodo.18109761
Paper 10	TEP-COS (This repo)	Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars	10.5281/zenodo.18165798
Paper 11	TEP-H0	The Cepheid Bias: Resolving the Hubble Tension	10.5281/zenodo.18209702
Paper 12	TEP-JWST	The Temporal Equivalence Principle: A Unified Resolution to the JWST High-Redshift Anomalies	10.5281/zenodo.19000827
Paper 13	TEP-WB	The Temporal Equivalence Principle: Density-Dependent Screening in Gaia DR3 Wide Binaries	10.5281/zenodo.19102062

Directory Structure

TEP-COS/
├── data/                          # Raw and processed data
│   ├── pulsars/                  # Pulsar reference data
│   ├── clusters/                 # Cluster structural parameters
│   ├── supernovae/               # Supernova data
│   └── apogee/                   # APOGEE stellar data
├── scripts/
│   ├── steps/                    # Analysis pipeline steps
│   ├── utils/                    # Shared utility functions
│   │   ├── logger.py            # Logging infrastructure
│   │   └── archive/             # Utility archives
│   └── run_pipeline.py          # Master pipeline script
├── results/
│   ├── outputs/                 # Analysis results (JSON, CSV, Tables)
│   └── figures/                 # Generated plots (PNG, PDF)
├── site/
│   ├── components/              # Manuscript HTML sections
│   └── figures/                 # Figures embedded in manuscript
├── logs/                        # Pipeline execution logs
├── README.md                    # This file
├── requirements.txt             # Python dependencies
└── reproduce_manuscript.py      # Legacy wrapper (deprecated)

Installation

# Clone repository
git clone https://github.com/matthewsmawfield/TEP-COS.git
cd TEP-COS

# Install dependencies
pip install -r requirements.txt

Essential Data Files

Pulsar Analysis:

• results/outputs/step_5_10_pulsar_population_controls.csv - Main pulsar dataset
• results/outputs/atnf_psrcat.db - ATNF pulsar catalog (auto-downloaded)
• results/outputs/freire_GCpsr.txt - Freire catalog (auto-downloaded)

Supernova Analysis:

• data/supernovae/pantheon_plus_parsed.csv - Pantheon+ SN Ia compilation

Reproduction Steps

This analysis focuses on pulsar timing in globular clusters.

Pulsar Timing Analysis

The pulsar analysis proceeds in stages: sample construction, population controls, and environmental testing.

Manuscript Section	Analysis Step	Script	Description
3.2	Sample Construction	step_5_27_hybrid_maximum_analysis.py	Generates the maximal MSP sample (GC + Field) from Freire/ATNF catalogs.
3.3	Population Controls	step_5_10_pulsar_population_controls.py	Applies period and B-field matching to isolate environmental residuals.
3.4	Density Scaling	step_5_31_per_cluster_controlled_residuals.py	Tests residual scaling against cluster density ($\rho_c$).
3.5	Newtonian Baseline	step_5_13_cluster_acceleration_figure.py	Simulates and plots raw acceleration broadening (Figure 4.5).
3.5	Density Scaling Sim	step_5_32_density_scaling_figure.py	Simulates and plots density scaling predictions (Figure 4.6).
3.7	Binary vs Isolated	step_5_11_binary_pulsar_analysis.py	Tests binary vs isolated MSP residuals within GCs.
3.7	Binary Spatial Fig	step_5_11_binary_spatial_figure.py	Generates spatial distribution plot of binaries in GCs.
3.8	Field Control	step_5_12_field_binary_analysis.py	Control test: binary vs isolated MSPs in the field.
3.10	Radial Analysis	step_5_9_freire_gcpsr_radial_analysis.py	Analyzes radial trends within clusters.

Appendix & Fossil Probes

Manuscript Section	Analysis Step	Script	Description
App. A	SN Ia Stretch	step_7_0_sn_ia_stretch_test.py	Tests SN Ia light curve stretch vs host velocity dispersion.
5.x	Summary Figure	step_5_40_tep_summary_figure.py	Generates TEP cosmology summary figure.

Running the Full Pipeline

To reproduce all results and figures:

python3 scripts/run_pipeline.py

Command-line Options

python3 scripts/run_pipeline.py --only-core       # Fast mode: core analysis only
python3 scripts/run_pipeline.py --skip-validation # Skip long validation steps
python3 scripts/run_pipeline.py --skip-figures    # Skip figure generation

This will populate results/outputs/ and results/figures/ with fresh data.

Legacy Script

For backward compatibility, reproduce_manuscript.py is preserved as a wrapper that calls scripts/run_pipeline.py.

Citation

@article{smawfield2026tepcos,
  title={Temporal Equivalence Principle: Suppressed Density Scaling in Globular Cluster Pulsars},
  author={Smawfield, Matthew Lukin},
  year={2026},
  doi={10.5281/zenodo.18165798},
  url={https://doi.org/10.5281/zenodo.18165798},
  note={Preprint v0.5 (Caracas)}
}

---

Open Science Statement

These are working preprints shared in the spirit of open science—all manuscripts, analysis code, and data products are openly available under Creative Commons and MIT licenses to encourage and facilitate replication. Feedback and collaboration are warmly invited and welcome.

---

Contact: matthewsmawfield@gmail.com
ORCID: 0009-0003-8219-3159