Appendix B: SPARC Data Processing Scripts

This appendix documents the data-processing pipeline used to analyze galactic rotation curves from the SPARC database. All steps are explicitly defined to ensure full reproducibility and transparency.

B.1 Data Input and Preprocessing

The SPARC database provides, for each galaxy, radial profiles of observed rotation velocity, baryonic contributions, and associated uncertainties.

function load_sparc_galaxy(file):
    r, v_obs, v_gas, v_disk, v_bulge = read_columns(file)
    return r, v_obs, v_gas, v_disk, v_bulge

All radii are converted to meters and velocities to SI units. Galaxies with incomplete or flagged data are excluded.

B.2 Computation of Accelerations

Observed and baryonic accelerations are computed as:

with

function compute_accelerations(r, v_obs, v_gas, v_disk, v_bulge):
    v_bar2 = v_gas**2 + v_disk**2 + v_bulge**2
    a_obs = v_obs**2 / r
    a_bar = v_bar2 / r
    return a_obs, a_bar

No dark matter halo model is assumed at any stage.

B.3 Quality Cuts and Error Handling

Data points are filtered to avoid numerical artifacts:

• inner radii below resolution limits are excluded,
• points with large fractional velocity errors are discarded,
• non-physical values are removed.

mask = (r > r_min) and (error_v / v_obs < threshold)
a_obs = a_obs[mask]
a_bar = a_bar[mask]

These cuts follow standard SPARC analysis practices.

B.4 Fitting the Radial Acceleration Relation

The functional form used is:

function fit_a_star(a_obs, a_bar):
    minimize scatter in log(a_obs) - log(f(a_bar, a_star))
    return best_fit_a_star

The fit is global across all galaxies. No galaxy-dependent parameters are introduced.

B.5 Bootstrap Analysis

Statistical robustness is assessed via bootstrap resampling:

for k in range(N_bootstrap):
    resampled_galaxies = sample_with_replacement(galaxy_list)
    a_star[k] = fit_a_star(resampled_data)

The resulting distribution of $a_*$ is used to compute confidence intervals.

B.6 Output Products

The analysis outputs:

• scatter plots of $a_{\rm obs}$ vs. $a_{\rm bar}$,
• best-fit curves with confidence bands,
• bootstrap distributions of $a_*$,
• summary tables for each galaxy.

All plots shown in the main text are generated directly from these scripts.

Note: The same pipeline can be applied to future rotation-curve datasets without modification, providing a direct avenue for independent verification or falsification of the framework.