>[!warning] >This content has not been peer reviewed. # SPARC Evaluation — Method and Data The RST gravity sector is evaluated against galaxy rotation curves. This note documents the **method** and the **data source**; for results see **[[SPARC Evaluation Verification]]** and **[[SPARC Evaluation Results]]**. **Implementation:** The code that runs the pipeline (rawt package + notebooks) lives in **[[about systems/expanded theory/sparc evaluation/README|expanded theory/sparc evaluation/]]**. It uses the shared **rst_engine** for $\mu(\eta,n)$ and the generic solver; see **[[about systems/expanded theory/sparc evaluation/SPARC evaluation - Code]]**. --- ## Data source and citation **SPARC database:** [http://astroweb.cwru.edu/SPARC/](http://astroweb.cwru.edu/SPARC/) **Citation:** Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016). SPARC: Mass models for 175 disk galaxies with Spitzer photometry and accurate rotation curves. *The Astronomical Journal*, 152, 157. [arXiv:1606.09251](https://arxiv.org/abs/1606.09251) Download the rotation-curve data (e.g. rotmod files) from the SPARC site to reproduce or extend the evaluation. --- ## Method (pipeline logic) 1. **Inputs:** For each galaxy, observed gas, disk, and bulge give Newtonian acceleration $g_N(r)$. Fixed parameters: $a_0 = cH_0/(2\pi)$; $n$ derived from Pure Axiom Substrate (SPARC evaluates prediction). 2. **Solve:** RST field equation $\mu(q'/a_0,\, n)\, q' = g_N$ for $q'(r)$; predict $v(r) = \sqrt{r \cdot q'}$. 3. **Fit:** Single free parameter per galaxy: $\Upsilon_{\text{disk}}$ (mass-to-light). Minimise reduced $\chi^2$. No dark matter halo parameters. 4. **Outputs:** Per-galaxy $\Upsilon_{\text{disk}}$, $\chi^2$; aggregate statistics (e.g. 86% acceptable fits; median $\Upsilon_{\text{disk}}$ typically 0.49–0.52 depending on run — see [[SPARC Evaluation Results]]). --- ## Core relations used - **$\mu(\eta, n)$:** $\mu = \eta/(1+\eta^n)^{1/n}$ with $\eta = \Omega/N$. - **Solve for $g_{\text{obs}}$:** From $g_N = g_{\text{obs}}^2 / (g_{\text{obs}}^n + a_0^n)^{1/n}$ (root-finding). - **Cosmology:** $a_0(z) = cH(z)/(2\pi)$, $n(z) = n_0 + \ln(H(z)/H_0)$ for high-$z$ predictions. See **[[Noise Floor]]**, **[[Fidelity]]**, **[[Transition Sharpness]]** for definitions. --- ## Where the code lives | What | Where | |:---|:---| | **Pipeline (rawt + notebooks)** | **[[about systems/expanded theory/sparc evaluation/README]]** — `sparc evaluation/rawt/`, `sparc evaluation/notebooks/` | | **Engine** | `rst_engine/` at workspace root (same as applications) | | **Outputs** | `sparc evaluation/notebooks/output/` (plots, CSV) | | **Code note (implementation)** | **[[about systems/expanded theory/sparc evaluation/SPARC evaluation - Code]]** |