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

Authors / Creators Mustafa BabayigitIndependent Researcher, BelgiumORCID: 0009-0006-2933-281X Description Overview DISSIPATIVEDYNAMICSYSTEMV2 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 independent external galaxy validation into a unified staged analysis pipeline. The framework investigates 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 DISSIPATIVEDYNAMICSYSTEMV2 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, independent external validation using LITTLE THINGS dwarf galaxies, and independent McGaugh/LSB external validation. 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, independent McGaugh/LSB external 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, adaptive regime-switch validation, information-criteria model comparison, and flow-state phenomenological reconstruction. 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. New in This Release This updated release includes an additional independent external validation using the McGaugh/LSB galaxy compilation containing 671 radial measurements across 48 galaxies. The new validation phase demonstrates that flow-sensitive and dissipative regime-aware corrections systematically outperform purely morphology-sensitive corrections under Akaike and Bayesian information-criteria analysis. The external validation substantially strengthens the interpretation that an important fraction of residual RAR structure is associated with organized dynamical-support and flow-state phenomenology rather than purely static galaxy morphology alone. This release also includes: updated main manuscript revisions, expanded supplementary validation material, improved reproducibility infrastructure, naturally sorted execution order for staged pipelines, updated automated supplementary-generation framework, improved manuscript consistency and terminology, revised reproducibility ZIP generation, and improved end-to-end pipeline reproducibility validation. 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 preliminaryᵢnvestigationDISSIPATIVEDYNAMICSYSTEM_. pdf preliminaryᵢnvestigationDISSIPATIVEDYNAMICSYSTEMᵣeproducibilityₚackage. zip DISSIPATIVEDYNAMICSYSTEMV2ᵣeproducibility_*. 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, reproducibility manifests, reproducibility ZIP archives, and manuscript outputs. Main Outputs Main manuscript main. pdf Supplementary materials supplementary. pdf Preliminary investigation preliminaryᵢnvestigationDISSIPATIVEDYNAMICSYSTEM_. pdf Representative figures results/figures/paperfigures/figure1ₚhaseₜransitionₘap. pdf Repository Structure data/scripts/results/paper/config/environment/tests/run. shMakefileREADME. mdLICENSE Author Mustafa BabayigitIndependent Researcher, Belgium ORCID: 0009-0006-2933-281XEmail: mustafa. babayigit@outlook. be 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.