Reproducible Instability-Axis Reconstruction and Regime-Dependent RAR Analysis in Disk Galaxies

Overview DISSIPATIVE_DYNAMIC_SYSTEM_V2 is a fully reproducible computational astrophysics research framework investigating structured dynamical regimes in disk galaxies through empirical instability-axis reconstruction, regime-dependent Radial Acceleration Relation (RAR) analysis, and dynamical manifold organization. The project combines empirical galaxy dynamics, reproducible statistical reconstruction, robustness validation, synthetic falsification testing, and external dwarf-galaxy validation into a unified staged analysis pipeline. The framework was designed to investigate whether part of the observed RAR residual structure reflects organized dynamical-regime behavior rather than purely stochastic scatter. Importantly, the analysis remains fully phenomenological and empirical. The project does not claim: a replacement for dark matter, a new theory of gravity, or a fundamental modification of General Relativity. Instead, the reconstructed instability coordinate χ acts as an empirical regime-tracking coordinate associated with coupled baryonic structure, dynamical support, residual-flow organization, and halo-sensitive phenomenology. Preliminary Investigation and Scientific Evolution The present archive builds upon an earlier empirical dynamical-systems investigation of galaxy populations documented in the preliminary study: "Empirical Dynamical Systems Structure in Galaxy Populations: Attractors, Runaway Regimes, and Dissipative Manifolds." The preliminary investigation reconstructed galaxy populations as an empirical dynamical manifold using: manifold reconstruction, attractor-basin analysis, sparse operator discovery, Jacobian stability diagnostics, hysteresis reconstruction, Koopman spectral analysis, bifurcation testing, and synthetic null-universe falsification. The preliminary analysis revealed several important empirical structures: compact spiral-galaxy attractor basins, metastable transition layers, runaway high-spread dwarf regimes, and bifurcation-like organization associated with nonlocal spread observables. A dominant empirical transition scale emerged near: Sc ≈ 3.74 separating low-spread attractor behavior from dynamically stressed runaway regimes. The present DISSIPATIVE_DYNAMIC_SYSTEM_V2 framework extends and refines this earlier phenomenological reconstruction into a leakage-safe, reproducible, and regime-dependent RAR analysis framework centered on the reconstructed Galactic Instability Axis χ. While the preliminary investigation focused primarily on global dynamical-manifold organization, the current archive focuses on: structured RAR residual organization, instability-axis reconstruction, galaxy-family dynamics, regime-dependent corrections, robustness validation, synthetic falsification testing, and independent external validation using LITTLE THINGS dwarf galaxies. The preliminary investigation therefore represents the conceptual and empirical foundation from which the present instability-axis framework evolved. Scientific Components The pipeline integrates: SPARC galaxy database analysis, independent LITTLE THINGS dwarf-galaxy validation, leakage-safe manifold reconstruction, hidden-subfamily detection, family-transfer validation, bootstrap robustness analysis, leave-one-galaxy-out validation, synthetic-universe falsification, randomized topology destruction tests, instability-manifold reconstruction, residual-flow diagnostics, bifurcation stress reconstruction, regime-dependent RAR correction modeling, halo-sensitive empirical extensions, and adaptive regime-switch validation. The analysis framework contains 51 sequential reconstruction and validation stages executed through a unified reproducibility pipeline. Main Scientific Results The project reconstructs an empirical Galactic Instability Axis χ that systematically organizes galaxy populations into structured dynamical regimes including: stable-support systems, transition-zone galaxies, and unstable-flow / dynamically stressed regimes. A reproducible bifurcation-like transition emerges near: χc ≈ 2.22 where RAR residual stress, dynamical instability, and manifold dispersion increase significantly. The framework demonstrates that a substantial fraction of observed RAR residual organization is structured rather than purely stochastic. The reconstructed instability manifold generalizes successfully to the independent LITTLE THINGS dwarf-galaxy sample without retraining. The project further demonstrates that incorporating regime-state information into phenomenological RAR modeling improves the organization of dynamically stressed systems, particularly in dwarf and low-support galaxy populations. Included Contents The archive contains: complete analysis scripts (Stages 01 → 51), processed datasets, machine-readable output tables, publication-ready figures, manifold reconstruction diagnostics, bootstrap and robustness outputs, synthetic falsification tests, supplementary analysis infrastructure, automated manuscript generation, the main scientific manuscript, supplementary materials, the preliminary dynamical-systems investigation, and full reproducibility infrastructure. Included files: main.pdf supplementary.pdf preliminary_investigation_DISSIPATIVE_DYNAMIC_SYSTEM_.pdf preliminary_investigation_DISSIPATIVE_DYNAMIC_SYSTEM_reproducibility_package.zip DISSIPATIVE_DYNAMIC_SYSTEM_V2_reproducibility_20260518T234438Z.zip Reproducibility The complete project can be reproduced through the automated reconstruction pipeline: ./run.sh The workflow automatically regenerates: processed datasets, statistical tables, publication figures, validation diagnostics, supplementary materials, and manuscript outputs. Main Outputs Main manuscript: main.pdf Supplementary materials: supplementary.pdf Preliminary investigation: preliminary_investigation_DISSIPATIVE_DYNAMIC_SYSTEM_.pdf Representative figures: results/figures/paper_figures/figure1_phase_transition_map.pdf Repository Structure data/ scripts/ results/ paper/ config/ environment/ tests/ run.sh Makefile README.md LICENSE Author Mustafa BabayigitIndependent Researcher, Belgium ORCID: 0009-0006-2933-281XEmail: [email protected] Website:https://irmustafababayigit.github.io Citation If you use this archive, please cite the associated Zenodo record and accompanying manuscript. License This project is released under the MIT License. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated research materials to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the project, subject to the conditions of the MIT License. The archive is provided for scientific research, reproducibility, independent validation, educational use, and further methodological development. See the included LICENSE file for the complete license text.