Author: Matthew Lukin Smawfield
Version: v0.3 (New Delhi)
Date: First published: 28 December 2025 · Last updated: 29 April 2026
Status: Preprint
DOI: 10.5281/zenodo.18064365
Website: https://matthewsmawfield.github.io/TEP-UCD/
Dark matter observations across cosmological scales exhibit a regularity: the characteristic radius at which Newtonian dynamics fails scales as R ∝ M^(1/3), implying a universal critical density ρ_T. This scaling appears in galaxy rotation curves (SPARC database), ultra-diffuse galaxies (DF2/DF4), the Milky Way's Keplerian transition, and compact object phenomena (magnetar anti-glitches). This pattern is shown to reflect a fundamental saturation scale in the conformal time-field sector of the Temporal Equivalence Principle (TEP), where gravitational solitons form at a characteristic saturation density.
Terrestrial calibration—derived from a newly identified distance-structured correlation in GNSS atomic clocks—provides an independent measurement of this scale. Multi-center analysis (CODE, IGS, ESA) reveals correlations with characteristic length L_c ≈ 4200 km for Earth's mass (M_⊕ ≈ 6 × 10^27 g), implying ρ_T ≈ 20 g/cm³. This calibration exhibits 25-year temporal stability and survives raw RINEX validation, strongly constraining processing-artifact explanations.
Galactic-scale validation comes from the SPARC rotation curve database (175 galaxies). The empirical dark matter onset scaling is α = 0.354 ± 0.014, consistent with the M^(1/3) prediction within 2σ. Gaia DR3 analyses report evidence consistent with a Keplerian-like decline near R ≈ 19 kpc in the Milky Way, broadly consistent with the predicted transition scale. For ultra-diffuse galaxies DF2 and DF4, the model predicts soliton radii exceeding tidal radii, consistent with observed dark matter deficiency via tidal stripping of the scalar field envelope.
Temporal Topology screening resolves the apparent conflict with precision GR tests. Analysis of 26 astrophysical objects spanning 15 orders of magnitude in density reveals an empirical scaling S ∝ ρ^0.334 (R² = 0.9999), confirming the predicted ρ^(1/3) dependence. At nuclear densities (binary pulsars: ρ ~ 10^14 g/cm³), screening factors exceed S > 30,000, suppressing scalar contributions to less than 0.003% of orbital dynamics. This hierarchy explains why Solar System tests, binary pulsar timing, and gravitational wave observations show no deviation from GR, while galactic dynamics (ρ ~ 10^-24 g/cm³, S ~ 0.01) exhibit strong scalar effects.
Compact object consistency is assessed using magnetar anti-glitches. For a canonical neutron star mass (M ≈ 1.4 M_⊙) and ρ_T ≈ 20 g/cm³, the model predicts a critical spin period P_crit ≈ 6.8 s, below which the soliton radius exceeds the stellar radius. The magnetar 1E 2259+586 (P = 6.98 s) exhibits anti-glitch behavior, consistent with this threshold within 4%.
The saturation density ρ_T ≈ 20 g/cm³ emerges as a candidate universal saturation scale of the temporal-field topology — not an ambient-density switch — supported by cross-scale consistency across 40 orders of magnitude in mass (proton to galaxy cluster) and 15 orders of magnitude in density (cosmological voids to neutron stars), within stated uncertainties. This externally calibrated value enables tightly constrained astrophysical applications, including the RBH-1 runaway black hole candidate (companion paper).
A universal critical density ρ_T ≈ 20 g/cm³ organizes gravitational anomalies across 15 orders of magnitude. Terrestrial calibration from GNSS atomic clocks (L_c ≈ 4,200 km) provides an independent anchor consistent with galactic-scale observations (SPARC rotation curves: α = 0.354 ± 0.014, consistent with M^(1/3) prediction within 2σ). Analysis of 26 astrophysical objects confirms the screening hierarchy follows S ∝ ρ^0.334 (R² = 0.9999). A dramatic prediction: magnetar anti-glitches should occur near P_crit ≈ 6.8 s for canonical neutron stars—confirmed by 1E 2259+586 (P = 6.98 s, 4% match).
| 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 Analysis of CODE Precise Clock Products | 10.5281/zenodo.17517141 |
| Paper 3 | TEP-GNSS-RINEX | Global Time Echoes: Raw RINEX Consistency Test | 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 Synthesis | 10.5281/zenodo.18004832 |
| Paper 6 | TEP-UCD (This repo) | Universal Critical Density: Cross-Scale Consistency of ρ_T | 10.5281/zenodo.18064365 |
| Paper 7 | TEP-RBH | The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate | 10.5281/zenodo.18059251 |
| Paper 8 | TEP-SLR | Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging | 10.5281/zenodo.18064582 |
| Paper 9 | TEP-EXP | What Do Precision Tests of General Relativity Actually Measure? | 10.5281/zenodo.18109760 |
| Paper 10 | TEP-COS | The 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: Temporal Shear Recovery in Gaia DR3 Wide Binaries | 10.5281/zenodo.19102061 |
-
site/components/: HTML components comprising the manuscript sections.-
1_abstract.html: Paper abstract. -
2_introduction.html: The Dark Matter problem as a temporal structure problem. -
3_gnss_calibration.html: Derivation of$\rho_T$ from atomic clocks. -
4_sparc_validation.html: Galactic rotation curve analysis. -
5_screening_hierarchy.html: Temporal Topology screening mechanism. -
6_atomic_boundary.html: Physical constraints on ρ_T (electron degeneracy, dimensional analysis). -
7_universal_scaling.html: The unified scaling law. -
8_magnetar_test.html: Magnetar anti-glitch validation. -
9_milky_way_test.html: Local Milky Way Keplerian transition. -
10_discussion.html: Theoretical implications (Phantom Mass). -
11_conclusion.html: Summary of findings. -
12_visual_evidence.html: Key figures. -
13_references.html: Bibliography. -
appendix_a_gnss.html: GNSS methodology appendix.
-
- Preceded by: Papers 0–4 and the Synthesis (TEP, TEP-GNSS series, TEP-GL, TEP-GTE), which establish the empirical reality of the clock correlations and the theoretical framework.
- Companion to: Paper 7 (TEP-RBH), which applies the ρ_T value derived here to test the soliton hypothesis for the runaway black hole candidate RBH-1.
@article{smawfield2025ucd,
title={Universal Critical Density: Unifying Scales},
author={Smawfield, Matthew Lukin},
journal={Zenodo},
year={2025},
doi={10.5281/zenodo.18064365},
note={Preprint v0.3 (New Delhi)}
}This project is licensed under Creative Commons Attribution 4.0 International (CC-BY-4.0). See LICENSE for details.
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: matthew@mlsmawfield.com
ORCID: 0009-0003-8219-3159
The manuscript is assembled from the HTML components in site/components/.