An Analytic Mathematical Model to Explain the Spiral Structure and Rotation Curve of NGC 3198
Bibliographic record
Abstract
This archive presents the source code, data, and full paper for a mathematical model explaining both the spiral morphology and flat velocity rotation profiles of disk galaxies. The model is derived from a transformation within general relativity, applied to rotating polar coordinate systems in a metric-preserving manner. It demonstrates that the observed flat rotation curves and spiral structures are natural products of relativistic frame dynamics—without invoking non-baryonic dark matter. The model has been tested against 878 galaxy rotation curves, primarily in the Southern Hemisphere, using datasets compiled by Salucci and others. Derived mass and angular momentum estimates are cross-validated with distance moduli from Cepheid variables, water masers, and Tully-Fisher relations. We show that the morphology of NGC 3198 aligns with a rotating geodesic and suggest that such galaxies are gravitationally viscous and self-bound systems. This archive includes the full text of the paper, raw and processed rotation curve data, Matlab source code, and README documentation for reproducibility.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".