Dynamical Information Geometry (DIG), Part IV: Regime Tests and Invariance — Data Set

This dataset accompanies Dynamical Information Geometry (DIG), Part IV and provides the complete numerical and hardware data used to investigate the regime structure, validity boundaries, and structural invariance properties of the DIG framework. DIG assigns an effective, state-dependent geometry to quantum many-body systems via the curvature of a coarse-grained mutual-information profile. While DIG Part I establishes the theoretical framework, DIG Part II provides numerical evidence for slowing and acceleration effects, and DIG Part III validates a minimal operational consequence on quantum hardware, the present dataset supports DIG Part IV by documenting the stability and invariance properties of these sign-dependent modifications of operator propagation under controlled variations. The dataset includes raw and processed data from a collection of operationally defined tests performed under strictly energy-matched conditions. These tests probe sign structure, antisymmetry, regime boundaries, invariance under changes in system size or implementation, and robustness under local perturbations. Both numerical simulations and quantum-hardware executions are included where applicable. All data are provided without fitting, extrapolation, noise mitigation, or cross-platform normalization beyond the explicitly documented operational definitions. The archive is designed to enable independent verification, alternative analyses under clearly stated assumptions, and reproducibility audits. The dataset contains complete raw outputs, analysis and audit scripts, metric inventories, regime tables, and a detailed README describing folder structure, operational definitions, and verification procedures. Cryptographic checksums (SHA-256) are provided separately to ensure data integrity. Relation to the DIG program DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (numerical validation):https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG — N1 (definitions and scope):https://doi.org/10.5281/zenodo.18001179 DIG Part IV introduces no new theoretical constructs beyond these works. The dataset is intended to document the regime behavior and structural robustness of the DIG framework in an auditable and reproducible manner. Intended use This dataset is intended for independent verification of regime behavior, reproducibility checks, and comparative analysis under explicit operational choices. It is not intended as a benchmark for quantitative universality or parameter fitting. Correspondence regarding this dataset may be directed to: kaya@cab-film.com