The paper
This work analyzes SPARC galaxy rotation curves and shows that the inferred compressibility profiles κ(r) do not follow a universal law, but instead organize into a small number of distinct dynamical classes.
A central result is that, when re-expressed in terms of an accumulated structural variable S(r), these profiles become significantly more regular and define simple class-dependent relations κ(S), establishing S as a natural structural coordinate for the system.
The emergence of a transition scale Sc indicates that the dynamical discrepancy reflects organized structural regimes, suggesting that the observed complexity may largely arise from the choice of radial representation rather than intrinsic dynamical irregularity.
Current version:
emergent_gravity_v15_11.pdf
Project summary
The goal of this work is to explore whether the observed discrepancy between baryonic
and dynamical mass in galaxies may encode structured regimes rather than only an
additional matter component.
The key result is the emergence of class-dependent κ(S) relations and a characteristic
transition scale Sc.
Data and methods
Compressibility:
κ(r) = Vbar²(r) / Vobs²(r)
Structural variable:
S(r) = ∫₀ʳ | d log Vbar / dr′ | dr′
- SPARC dataset used
- κ(r) reconstructed for each galaxy
- Profiles classified into dynamical families
- Reparametrization using S(r)
- Class-dependent logistic κ(S) fits
- Robustness tested under Υ variations
News & Updates
April 2026: v15.11 released - the κ(S) representation is now established as the natural structural description of rotation curve discrepancies, replacing the radial view of v15.4.
The accumulated variable S emerges as the key coordinate where galaxy dynamics organize into regular, class-dependent profiles.
The transition scale Sc is identified as the fundamental threshold governing this structural reorganization.
April 2026: v15.4 released — introduction of S(r),
κ(S) relations, and robustness analysis.