Dynamical Information Geometry IV: Regime Structure, Structural Invariance, and an Operational No-Escape Result

Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work establishes the regime structure, structural invariance, and an operational no-escape result for the Dynamical Information Geometry (DIG) framework. DIG assigns an effective, state-dependent information geometry to quantum many-body systems via the curvature of a coarse-grained mutual-information profile. Earlier work introduced the theoretical framework, provided numerical evidence for slowing and acceleration of operator fronts, and validated a minimal operational consequence on quantum hardware. The present work addresses a distinct question: Which structural and operational consequences follow from the Twin Test observations under the assumptions of unitary dynamics, finite information propagation, and compositionality? This manuscript introduces no new theoretical framework, equations of motion, fits, or scaling laws. Instead, it consolidates and hardens the operational consequences of DIG by: establishing that the DIG response exists only within a finite onset–window–breakdown regime; demonstrating form invariance of the response across implementations (system size, architecture, and hardware platform); introducing mandatory operational audits and a deterministic observable-selection rule that prevents the misreading of the Twin Test as marker persistence; formulating an operational no-escape result: within the Twin-protocol class, any explanation compatible with unitary dynamics, finite information propagation, and compositionality necessarily induces a state-dependent information-geometric cost structure. The Twin Test is treated as a structured existence test, not a statistical procedure. All reported results are sign-based and strictly operational. No fitting, extrapolation, noise mitigation, or cross-platform normalization is applied. The work documents Twin-Test realizations on heterogeneous quantum hardware platforms, including superconducting qubits and trapped-ion systems, and shows that apparent discrepancies (such as marker transfer on specific devices) are regime-diagnostic rather than failures, indicating that DIG operates as a bounded phenomenon. All numerical and hardware results reported in this paper are fully reproducible from the accompanying public dataset without additional assumptions. For reference and context, related DIG materials include: 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 Dataset:https://doi.org/10.5281/zenodo.18198830 DIG Part V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (scaling 1D hardware validation): https://doi.org/10.5281/zenodo.18226369 DIG Part VII Dynamical Information Geometry:Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraintshttps://doi.org/10.5281/zenodo.18313460 DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 Correspondence regarding this work may be directed to:[email protected]