RFT v2 Galaxy Rotation Curves

Predictive modeling with zero per-galaxy tuning (k=0)

k=0 Fair Comparison
58.8%
Pass rate on TEST galaxies (20/34) with zero per-galaxy parameters

RFT v2

58.8%
20/34 galaxies pass
k=0 (no tuning)

NFW (Global)

52.9%
18/34 galaxies pass
k=0 (no tuning)

MOND

23.5%
8/34 galaxies pass
k=0 (no tuning)

What Does k=0 Mean?

In galaxy rotation fitting, k represents the number of free parameters tuned per individual galaxy. Traditional approaches often use k=2 or more (e.g., fitting both mass-to-light ratio and halo concentration for each galaxy).

The Fairness Problem

When you tune 2+ parameters per galaxy, you're essentially fitting the data rather than predicting it. A model with enough free parameters can fit almost anything. k=0 means the same global parameters are used for all galaxies - no per-galaxy tuning allowed.

RFT v2 uses a single set of parameters derived from the TRAIN split (85 galaxies) and applies them unchanged to the TEST split (34 galaxies). This is the only fair way to compare predictive power.

Methodology

  • Dataset: SPARC database (175 galaxies with high-quality rotation curves)
  • Split: 85 TRAIN / 56 VALIDATION / 34 TEST (stratified by morphology)
  • Pass criterion: RMS residual below 20% of observed velocity
  • Frozen config: rc-v2-green-20pct (commit 3428db0f)
  • Statistical tests: Wilson confidence intervals, z-tests for significance

Head-to-Head Results (k=0)

Model Pass Rate Galaxies Parameters (k) Wilson 95% CI
RFT v2 58.8% 20/34 0 [41.0%, 74.4%]
NFW (Global) 52.9% 18/34 0 [36.2%, 68.9%]
MOND 23.5% 8/34 0 [11.4%, 41.6%]

Note: NFW with per-galaxy fitting (k=2) achieves 82.4%, but this is not a fair comparison since it uses 2 free parameters per galaxy.

The Physics Behind RFT v2

RFT v2 models galaxy rotation through resonant field dynamics in curved spacetime. Instead of invoking dark matter halos, the theory predicts that spacetime geometry itself produces the "missing" centripetal acceleration through scalaron-mediated effects.

The key insight: the same field equation that governs particle physics at quantum scales also applies at galactic scales, with appropriate dimensional scaling. This unification is what allows a k=0 approach - the physics is determined by the theory, not fitted to data.

Resources

PDF Draft Paper GitHub Source Code

Verify It Yourself

The solver includes an independent auditor that verifies all claims:

git clone https://github.com/RFT-Cosmology/rft-v2-galaxy-rotations
cd rft-v2-galaxy-rotations
python3 audit/audit_all.py

The auditor checks data integrity, validates statistical tests, and confirms the headline numbers without requiring trust in our code.

Citation

@software{rft_v2_galaxy_rotations,
  title={RFT v2 Galaxy Rotation Curves: Predictive k=0 Modeling},
  author={RFT Cosmology Collaboration},
  year={2025},
  version={2.2.2},
  url={https://github.com/RFT-Cosmology/rft-v2-galaxy-rotations}
}