Author: Matthew Lukin Smawfield
Version: v0.3 (Kathmandu)
Date: 17 December 2025
Status: Preprint
DOI: 10.5281/zenodo.17860166
Website: https://mlsmawfield.com/tep/gnss-iii/
This paper validates that distance-structured correlations in GNSS clocks exist in raw observations, not just processed products—eliminating the processing artifact hypothesis. Prior TEP analyses relied on precise orbit and clock products from global analysis centers, leaving open the possibility that observed signatures were artifacts of sophisticated processing chains. This paper addresses that concern by detecting distance-structured signatures in raw GNSS observations processed using Single Point Positioning (SPP) with broadcast ephemerides as the primary methodology, supplemented by precise ephemeris validation. Analysis of 539 globally distributed stations over 3 years (2022–2024, comprising 1.17 billion pair-samples across three independent filtering strategies) achieves 100% signal detection (72/72 metric combinations) with mean R² = 0.93, revealing directionally-structured correlations consistent with CODE's 25-year PPP findings (p < 10⁻¹⁵).
The primary finding is directional anisotropy: East-West correlations are 2–5% (MSC) to 22% (Phase Alignment) stronger than North-South at short distances (<500 km), with t-statistics up to 112 and Cohen's d up to 0.304. Month-by-month stratification shows stable polarity (E-W > N-S) at the 94–100% level across modes and metrics (worst case 34/36 months), consistent with a persistent underlying effect. A critical audit indicates this is not an artifact of distance distribution: E-W pairs are actually 13 km longer than N-S pairs (bias against signal), and robust distance-matching strengthens the ratio (1.033 → 1.041). At full distances, raw λ ratios can appear suppressed by distance-dependent biases; a geometry-corrected comparison yields ratios of 1.80–1.86, within 17% of CODE's benchmark (2.16).
Key validations include: (1) orbital velocity coupling detected at 3.2–5.4σ (best: r = −0.763), replicating CODE's 25-year finding (r = −0.888), with signal persisting under ionospheric removal (best ionofree: r = −0.416, 2.5σ); (2) position jitter and clock bias show similar orbital coupling (Δ ≈ 5%), consistent with spacetime—not just temporal—modulation; (3) CMB frame alignment at RA = 188°, Dec = −5° (20.0° from CMB dipole), matching CODE's benchmark (18.2°), with Solar Apex disfavored (86.5° separation); (4) geomagnetic stratification using real GFZ Kp data shows near-invariance at the primary threshold (Kp < 3 vs. Kp ≥ 3; median Δλ ≈ −1%); (5) year-specific planetary event modulation detected (2.8× above null, p < 0.001) with no consistent tidal GM/r² scaling, consistent with alignment-driven geometric coupling rather than tidal forcing.
This paper constitutes Paper 3 of the TEP-GNSS Research Series. Together with Paper 1 (multi-center validation) and Paper 2 (25-year temporal stability), these three complementary analyses—using different data sources, processing chains, and time periods—provide consistent evidence for planetary-scale, directionally-structured correlations in GNSS clock measurements.
| 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 (This repo) | 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 |
| Synthesis | TEP-GTE | Global Time Echoes: Empirical Validation of the Temporal Equivalence Principle | 10.5281/zenodo.18004832 |
| Paper 7 | TEP-UCD | Universal Critical Density: Unifying Atomic, Galactic, and Compact Object Scales | 10.5281/zenodo.18064366 |
| Paper 8 | TEP-RBH | The Soliton Wake: A Runaway Black Hole as a Gravitational Soliton | 10.5281/zenodo.18059251 |
| Paper 9 | TEP-SLR | Global Time Echoes: Optical Validation of the Temporal Equivalence Principle via Satellite Laser Ranging | 10.5281/zenodo.18064582 |
When using this code or results, please cite the paper and data sources listed below.
This project uses publicly available GNSS data from the following sources:
- Source: NASA Crustal Dynamics Data Information System (CDDIS)
- Archive: https://cddis.nasa.gov/archive/gnss/data/daily/
- Format: RINEX 2/3 (Hatanaka compressed)
Required Citation:
The data used in this study were acquired as part of NASA's Earth Science Data Systems and archived and distributed by the Crustal Dynamics Data Information System (CDDIS).
Reference:
Noll, C.E. (2010). The Crustal Dynamics Data Information System: A resource to support scientific analysis using space geodesy. Advances in Space Research, 45(12), 1421-1440. DOI: 10.1016/j.asr.2010.01.018
- Provider: International GNSS Service (IGS)
- Website: https://igs.org/
Required Citation:
Johnston, G., Riddell, A., & Hausler, G. (2017). The International GNSS Service. In P.J.G. Teunissen & O. Montenbruck (Eds.), Springer Handbook of Global Navigation Satellite Systems (1st ed., pp. 967-982). Springer International Publishing. DOI: 10.1007/978-3-319-42928-1
- Software: RTKLIB v2.4.3 (demo5 branch)
- Author: Tomoji Takasu
- Repository: https://github.com/tomojitakasu/RTKLIB
- Note: RTKLIB is no longer bundled. Install independently and ensure
rnx2rtkpis available in your PATH or at a configurable location.
Required Citation:
Takasu, T. (2009). RTKLIB: Open Source Program Package for RTK-GPS. FOSS4G 2009 Tokyo, Japan, November 2, 2009.
# One-command full pipeline (Step 1.0 + Step 2.x)
python run_full_analysis.py --filters optimal_100 dynamic_50
# Manual invocation (if needed)
python scripts/steps/step_1_0_data_acquisition.py
python scripts/steps/step_2_0_raw_spp_analysis.py| Step | Script | Description |
|---|---|---|
| 1.0 | step_1_0_data_acquisition.py |
Download RINEX → RTKLIB SPP → compact NPZ |
| 1.1 | step_1_1_generate_dynamic_50_metadata.py |
Generate quality-filtered station list |
| 2.0 | step_2_0_raw_spp_analysis.py |
Core exponential decay analysis |
| 2.1 | step_2_1_control_tests.py |
Regional & elevation stratification |
| 2.2 | step_2_2_anisotropy_analysis.py |
Directional (E-W vs N-S) anisotropy |
| 2.3 | step_2_3_temporal_analysis.py |
Year-by-year & seasonal stability |
| 2.4 | step_2_4_null_tests.py |
Solar/lunar/shuffle validation |
| 2.5 | step_2_5_orbital_coupling.py |
Orbital velocity correlation |
| 2.6 | step_2_6_planetary_events.py |
Planetary conjunction/opposition |
| 2.7 | step_2_7_cmb_frame_analysis.py |
CMB frame grid search |
Dataset: 539 stations × 3 years (2022–2024) = 1.17 billion pairs
| Mode | λ (km) | R² | Interpretation |
|---|---|---|---|
| Baseline (GPS L1) | 727 | 0.971 | Ionosphere included |
| Ionofree (L1+L2) | 1,072 | 0.973 | Ionosphere removed |
| Multi-GNSS | 815 | 0.928 | All constellations |
Key Findings (4 Pillars):
- Orbital Velocity Coupling: r = −0.763 (5.4σ), independently replicating CODE's 25-year finding (r = −0.888).
- CMB Frame Alignment: Best-fit at RA = 188°, Dec = −5° (20.0° from CMB dipole, matching CODE's 18.2°). Solar Apex disfavored (86.5° separation).
- Spacetime Symmetry: Position jitter and clock bias exhibit identical orbital coupling (Δ ≈ 5%), consistent with spacetime metric fluctuation.
- Planetary Modulation: Coherence modulation detected around 37 planetary events (2.8× above null, p < 0.001) with no tidal GM/r² scaling, ruling out tidal forcing.
Validation:
- Directional Anisotropy: E-W > N-S at short distances (<500 km): Coherence 1.033, Phase Alignment 1.224 (p < 10⁻¹⁵).
- Temporal Stability: E-W > N-S detected in 94–100% of all 36 months across all processing modes.
- Geometry-Corrected Ratio: 1.80–1.86 (matches CODE's 2.16 within 17%).
- Geomagnetic Independence: Signal invariant under storm conditions (Kp<3 vs Kp≥3: median Δλ ≈ −1%).
- Filter Independence: All three station filters converge to consistent results (CV < 15%).
CODE Cross-Validation: Ionofree λ = 4,811 km (2024) matches CODE's 25-year benchmark (4,201 ± 1,967 km)
TEP-GNSS-RINEX/
├── scripts/
│ ├── steps/ # Analysis pipeline (step_1_*, step_2_*)
│ └── utils/ # Shared utilities (config, logger, etc.)
├── site/ # Academic manuscript site
│ ├── components/ # HTML section files
│ ├── public/ # Static assets (favicon, images)
│ └── dist/ # Built site output
├── data/
│ ├── nav/ # Broadcast navigation files
│ ├── processed/ # Station metadata JSON
│ └── sp3/ # Precise orbits (optional)
├── results/
│ ├── figures/ # Generated plots (PNG)
│ └── outputs/ # Analysis results (JSON)
├── logs/ # Step execution logs
├── manuscript-rinex.md # Auto-generated markdown
└── VERSION.json # Version metadata
- RTKLIB v2.4.3 (demo5 branch) installed independently; ensure
rnx2rtkpbinary is in your PATH or specify its location in the environment/config. - Python packages: numpy, scipy, pandas, matplotlib, tqdm
- CDDIS authentication credentials (set
CDDIS_USER/CDDIS_PASSor configure.netrc)
- Processing: RTKLIB SPP with broadcast ephemerides (no precise products)
- Modes: Baseline (GPS L1), Ionofree (L1+L2), Multi-GNSS (GPS+GLO+GAL+BDS)
- Filters: ALL_STATIONS (539), OPTIMAL_100 (100 balanced), DYNAMIC_50 (clock std < 50 ns)
- Coherence: Magnitude-weighted phase coherence, inverse-variance weighted fitting
- Related: Paper 1 (Multi-Center) · Paper 2 (25-Year CODE)
@article{smawfield2025rinex,
title={Global Time Echoes: Raw RINEX Validation of Distance-Structured Correlations in GNSS Clocks},
author={Smawfield, Matthew Lukin},
journal={Zenodo},
year={2025},
doi={10.5281/zenodo.17860166},
note={Preprint v0.4 (Kathmandu)}
}This project is distributed under the Creative Commons Attribution 4.0 International License (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.
- NASA CDDIS for data distribution
- International GNSS Service (IGS) and contributing station operators
- Tomoji Takasu (RTKLIB)