Velocity-Dependent Suppression of an Empirical Dark-Matter Relaxation Signature

Description

Methods (English)

Methodological Documentation: Exploratory Framework Development

This work emerged from an exploratory, AI-assisted research workflow that
combined conceptual inquiry, empirical data analysis, and classical statistical
methods. The approach is documented here to ensure transparency regarding the
origin, scope, and limitations of the results.

1. Conceptual origin and problem framing

The project was initiated by theoretical and conceptual considerations
concerning the non-random nature of galactic structure and the observed diversity
of inner rotation curves.
These considerations motivated a qualitative exploration of relaxation,
timescales, and cumulative dynamical processing in disk galaxies.

Large language models were used as structured dialogue tools to support
brainstorming, conceptual clarification, and the formulation of testable
questions. They served as interactive assistants in the early ideation phase
but did not replace physical reasoning or empirical validation.

2. Empirical foundation and data processing

All quantitative analysis is based exclusively on publicly available
observational data from the SPARC database, comprising 175 disk galaxies with
well-measured rotation curves and mass models.

Under direct author supervision, Python-based analysis scripts were developed
to extract kinematic quantities and to construct derived observables relevant
to the study. No simulated or synthetic data were used at any stage.

3. Iterative derivation of empirical relations 

Guided by the initial conceptual framework, empirical relations were formulated and iteratively tested against the SPARC dataset.
This process led to the identification of statistically significant correlations
that had not been explicitly highlighted in prior analyses.

4. Emergence of the relaxation framework and saturation scale

The detected correlations (with a Spearman rank coefficient
ρ≃0.63\rho \simeq 0.63ρ≃0.63) revealed a characteristic change in behaviour at rotation
velocities of approximately 120 km s−1120\,\mathrm{km\,s^{-1}}120kms−1.

This observational feature motivated the introduction of an empirical
relaxation-based framework and the definition of discrete relaxation classes
(R-I to R-V), intended as a taxonomic ordering of galaxy dynamics rather than a
definitive physical model.

5. Technical implementation and consistency checks

All numerical calculations, statistical evaluations, and visualisations were
performed in Python using standard scientific libraries, including NumPy,
Pandas, Matplotlib, and SciPy where required.

Large language models were used to assist with code inspection, conceptual
consistency checks, and documentation refinement.
They were not used for data generation, numerical optimisation, statistical
inference, or simulation.

Scope and interpretation

The present work should be understood as an exploratory observational study and
an organisational proposal rather than a definitive physical explanation.
Its primary aim is to motivate further independent investigation,
reproducibility efforts, and professional follow-up by the scientific community.