21 SPARC Galaxy Test

A central strength of the present framework is its ability to confront observational data directly. In this section, we test the emergent-gravity predictions against high-quality galactic rotation-curve data from the SPARC database. The goal is to determine whether the informational dynamics reproduce the observed regularities without introducing new particles or free parameters.

21.1 Data Description

We use the SPARC (Spitzer Photometry and Accurate Rotation Curves) database, which provides high-resolution rotation curves for a large and diverse sample of disk galaxies. For each galaxy, SPARC includes:

• observed rotational velocities $v(r)$,
• baryonic contributions from stars and gas,
• reliable distance and inclination measurements.

The data span a wide range of masses, surface brightnesses, and morphologies, making SPARC an ideal testing ground for theories of galactic dynamics.

21.2 Extraction of a_\mathrmobs } and $a_{\mathrm{bar}}$

From the rotation curves, we compute the observed centripetal acceleration:

The baryonic acceleration is computed from the Newtonian contribution of visible matter:

where $v_{\mathrm{bar}}(r)$ is the rotation velocity expected from the observed distribution of stars and gas.

No assumptions about dark matter halos or modified force laws are introduced at this stage. Both quantities are extracted directly from the data.

21.3 Fitting Procedure

The informational framework predicts a nonlinear but universal relation between $a_{\mathrm{obs}}$ and $a_{\mathrm{bar}}$, governed by a characteristic acceleration scale $a_{\ast}$:

We adopt a functional form consistent with the emergent dynamics and widely used in the literature:

The parameter $a_{\ast}$ is determined by minimizing the scatter in logarithmic acceleration space across the full dataset. No galaxy-specific tuning is performed.

21.4 Bootstrap and Robustness

To assess statistical robustness, we perform a bootstrap analysis. Galaxies are resampled with replacement, and the fitting procedure is repeated for each resampled dataset.

This yields a distribution of best-fit values for $a_{\ast}$, allowing us to estimate confidence intervals and assess sensitivity to sample selection.

The resulting distribution is narrow, indicating that the extracted acceleration scale is not driven by outliers or specific subsamples.

21.5 Emergence of $a_\ast$

The analysis yields a characteristic acceleration scale:

This value emerges directly from the data. It is not imposed by the theory, nor calibrated using external constraints.

The tightness of the resulting Radial Acceleration Relation and the universality of $a_{\ast}$ across diverse galaxies provide strong empirical support for the informational framework. The same scale will reappear in independent contexts, providing further opportunities for falsification.

Having established consistency with galactic dynamics, we now turn to a second observational arena: gravitational-wave signals from black-hole mergers.