The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate

Author: Matthew Lukin Smawfield
Version: v0.3 (Blantyre)
Date: 28 December 2025 (Last updated: 29 April 2026)
Status: Preprint
DOI: 10.5281/zenodo.18059250
Website: https://mlsmawfield.com/tep/rbh/

Abstract

The runaway supermassive black hole RBH-1 ($z \approx 0.96$) presents a thermal paradox: JWST spectroscopy reveals a 650 km/s velocity discontinuity coexisting with cold, star-forming gas. Higher-resolution Keck/LRIS spectroscopy yields a narrow apex dispersion ($\sigma \approx 31 \pm 4$ km/s), far below the $\sigma \sim 80$–85 km/s expected if the emitting gas were predominantly at $T \sim 10^7$ K. Standard shock physics predicts post-shock temperatures $T \sim 10^7$ K, yielding a cooling time that exceeds the dynamical time by a factor of ~30. Yet the wake exhibits immediate star formation and extreme collimation (50:1 aspect ratio over 62 kpc).

RBH-1 is explored as a candidate Temporal Topology soliton/wake interpretation: a coherent region of altered proper-time rate. Under this candidate framing, the observed velocity discontinuity is reinterpreted as a metric shock (spatial gradient in gravitational redshift) rather than bulk thermalization, and the effective Jeans mass is reduced behind the front via time dilation, enabling immediate star formation without heating.

The characteristic temporal scale $R_T$, calibrated from terrestrial GNSS correlations (Smawfield 2025g), is applied as a consistency check rather than as proof that RBH-1 is a soliton. For RBH-1 ($M \approx 2 \times 10^7 M_\odot$), the calibration yields $R_T \approx 7.8 \times 10^7$ km $\approx 1.3 R_S$, comparable to the near-source transition scale, not the full 62 kpc wake length. The amplitude of the observed kinematic discontinuity depends on screening/transition physics (via $\beta_{\rm eff}$ at $R_{\rm trans}$) and is treated as an empirical constraint rather than an independent prediction. Specific falsification criteria are outlined; decisive discrimination awaits line-profile decomposition and X-ray flux limits.

Key Findings

RBH-1 (z ≈ 0.96) presents a thermal paradox: a 650 km/s velocity discontinuity coexists with cold, star-forming gas, yet standard shock physics predicts T ~ 10⁷ K requiring ~30× cooling time. JWST NIRSpec [O III] spectroscopy reveals narrow line widths (σ ~ 30 km/s vs expected ~85 km/s for thermal shock), supporting a cold "metric shock" interpretation rather than thermal shock. The temporal topology model predicts R_T ≈ 1.3 R_S with no free parameters—the scale is fixed by the universal critical density ρ_T ≈ 20 g/cm³ calibrated from terrestrial GNSS correlations, applied as a consistency check. This parameter-free prediction enables direct falsification via mass determination, X-ray flux limits, and line-profile decomposition.

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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 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	Universal Critical Density: Cross-Scale Consistency of ρ_T	10.5281/zenodo.18064365
Paper 7	TEP-RBH (This repo)	The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate	10.5281/zenodo.18059250
Paper 8	TEP-SLR	Global Time Echoes: Optical-Domain Consistency Test via Satellite Laser Ranging	10.5281/zenodo.18064581
Paper 9	TEP-EXP	What Do Precision Tests of General Relativity Actually Measure?	10.5281/zenodo.18109760
Paper 10	TEP-COS	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	Temporal Equivalence Principle: Temporal Shear Recovery in Gaia DR3 Wide Binaries	10.5281/zenodo.19102061

Theoretical Framework

This work builds on the Temporal Equivalence Principle (TEP), which proposes:

• Gravity is Geometry; Time is a Dynamical Field.
• The decomposition of proper time accumulation into "mass" and "time dilation" is gauge-dependent.
• Sector Decoupling: The Conformal Sector (clock rates) is unconstrained by GW170817, while the Disformal Sector (speed of transmission) is tightly bound.
• Soliton Solutions: The non-linear kinetic structure supports coherent field configurations ("Time Stars"), allowing for the macroscopic phenomenology observed in RBH-1.

TEP Theory Reference:

Smawfield, M. L. (2025). Temporal Equivalence Principle: Dynamic Time & Emergent Light Speed (v0.7 (Jakarta)). Zenodo. DOI: 10.5281/zenodo.16921911

File Structure

TEP-RBH/
├── scripts/
│   ├── utils/                      # Shared utilities
│   └── analyze_*.py                # Analysis scripts
├── site/                           # Academic manuscript site
│   ├── components/                 # HTML section files
│   ├── public/                     # Static assets
│   └── figures/                    # Generated plots
├── docs/                           # Related manuscripts
├── manuscript-rbh1.md              # Manuscript source
└── VERSION.json                    # Version metadata

Requirements

• Python 3.8+
• NumPy, SciPy, Matplotlib
• Astropy (for cosmological calculations)

See requirements.txt for complete dependencies.

Reproducibility

Install Dependencies

pip install -r requirements.txt

Generate All Figures

cd scripts/figures
python 01_wake_anatomy.py
python 07_polarization.py
python 09_line_width_test.py
python 10_wake_geometry.py
python 11_stellar_age.py
python 12_line_ratios.py
python 13_energy_budget.py

All figures are saved to site/figures/.

Run Key Analyses

python scripts/analysis_checks/cooling_calculation.py  # Validates cooling bottleneck
python scripts/analysis_checks/jeans_analysis.py       # Jeans length calculation
python scripts/analyze_line_profiles.py                # Line-profile decomposition
python scripts/run_rbh1_line_analysis.py              # Complete RBH-1 pipeline

Data Sources

• JWST NIRSpec Data: RBH-1 observations from van Dokkum et al. (2023, 2025)
  • Download via scripts/download_rbh1_data.py (auto-creates data/rbh1_jwst/)

Citation

@article{smawfield2025rbh1,
  title={The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate},
  author={Smawfield, Matthew Lukin},
  journal={Zenodo},
  year={2025},
  doi={10.5281/zenodo.18059250},
  note={Preprint v0.3 (Blantyre)}
}

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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.

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Contact: matthew@mlsmawfield.com
ORCID: 0009-0003-8219-3159