Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work builds on: C. Kaya and D. Buck,"Dynamical Information Geometry: Microscopic Foundations of Operator Refraction",Zenodo (2025), DOI: https://doi.org/10.5281/zenodo.17966909 This manuscript analyzes the positive information-curvature branch of the Dynamical Information Geometry framework and demonstrates controlled acceleration (advance) of operator fronts within Lieb–Robinson bounds. For reference and context, related DIG manuscripts include: DIG Part III (hardware validation of an operational consequence):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (finite regime structure and operational invariance):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):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 Note:A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179 This document clarifies definitions, scope, and conceptual boundaries of the DIG framework. DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work builds on: C. Kaya and D. Buck,"Dynamical Information Geometry: Microscopic Foundations of Operator Refraction",Zenodo (2025), DOI: https://doi.org/10.5281/zenodo.17966909 This manuscript analyzes the positive information-curvature branch of the Dynamical Information Geometry framework and demonstrates controlled acceleration (advance) of operator fronts within Lieb–Robinson bounds. For reference and context, related DIG manuscripts include: DIG Part III (hardware validation of an operational consequence):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (finite regime structure and operational invariance):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):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 Note:A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179 This document clarifies definitions, scope, and conceptual boundaries of the DIG framework. DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This preprint introduces Dynamical Information Geometry (DIG), a state-dependent geometric framework for operator spreading in one-dimensional quantum many-body systems. The central result is an emergent effective metric derived from the curvature of coarse-grained mutual information, leading to refraction-like modifications of operator front velocities independent of local energy density. The metric is obtained as the unique leading-order correction consistent with locality, parity symmetry, and dimensional analysis. For reference and context, related DIG manuscripts include: DIG Part II (“Positive Information Curvature and Acceleration of Operator Fronts”):https://doi.org/10.5281/zenodo.17982058 DIG Part III (“Hardware Validation of an Operational Consequence”):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):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 Part VIII (“Multidimensional Front Response Structures and Degenerate Twin-Sign Projections”): https://doi.org/10.5281/zenodo.18395775 DIG Part IX (Regime structure Twin-Sign): https://doi.org/10.5281/zenodo.18422925 DIG Part X (Intervention based "Killshot" closure) https://doi.org/10.5281/zenodo.18451913 DIG Part XI (Front Response Non-Reconstruction as a structural No-Go Result): https://doi.org/10.5281/zenodo.18462803 DIG Transpiler Dataset: https://doi.org/10.5281/zenodo.18451716 Note:A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179 This note fixes terminology, scope, and explicit non-equivalences of the Dynamical Information Geometry (DIG) framework and serves as a definitional anchor for the present work. DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 DIG - N3 (nullspace) https://doi.org/10.5281/zenodo.18654757 DIG - No Derivation https://doi.org/10.5281/zenodo.18392928 DIG in GIT https://doi.org/10.5281/zenodo.18632874 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This document (“N1”) fixes terminology, scope, and explicit non-equivalences for Dynamical Information Geometry (DIG). It serves as a definitions and scope anchor for the DIG framework. This note introduces no new analytical or numerical results and is intended solely to clarify definitions, scope, and conceptual boundaries of the DIG framework. For reference and context, related manuscripts include: • “Dynamical Information Geometry (DIG): A Symmetry-Derived Metric Governing Operator Refraction in Quantum Many-Body Systems”https://doi.org/10.5281/zenodo.17983399 • “DIG Part II – Numerical code and data for operator front dynamics”https://doi.org/10.5281/zenodo.17982058 DIG Part III (hardware validation of an operational consequence):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational context):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):https://doi.org/10.5281/zenodo.18210315 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work formulates the Dynamical Information Geometry (DIG) framework in spatial dimension d > 1. Dynamical Information Geometry assigns an effective, state-dependent geometry to quantum many-body systems. Earlier work focused on the one-dimensional setting, where the structure of the framework can be developed in its simplest and most transparent form. This manuscript states the multidimensional formulation of DIG explicitly. In dimensions higher than one, information-induced geometry is inherently multidirectional and cannot be reduced to a single scalar quantity associated with a preferred coordinate. Directionality and projection therefore enter as intrinsic structural aspects of the framework. The presentation is theoretical and structural in nature. It fixes the multidimensional formulation of Dynamical Information Geometry at the level of the framework itself and is not tied to particular realizations, implementations, or test scenarios. For reference and context, related DIG manuscripts 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 Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 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 — N1 (definitions, scope, and non-equivalences):https://doi.org/10.5281/zenodo.18001179 DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 This manuscript introduces no new theoretical framework beyond the existing DIG construction. Its role is to make explicit the multidimensional form implied by that construction and to fix its structural consequences at the level of the framework itself. Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This publication presents a hardware validation of a minimal, sign-based operational consequence of the Dynamical Information Geometry (DIG) framework on real quantum devices. The work introduces no new theory and no numerical modeling. Instead, it tests a single operational hypothesis (OD-DIG-H1) on heterogeneous quantum hardware platforms, including IBM Quantum and AWS Braket (IonQ). The operational quantity tested is the sign of the leakage differenceΔLeak = Leak_LENS − Leak_CTRL,with leakage defined as Leak = 1 − P(b_ref). The reference bitstring is defined per run as b_ref = mode(CTRL), ensuring a hardware-agnostic reference choice. For all included hardware runs, the observed sign of ΔLeak is positive under the stated operational definition. The analysis is deliberately restricted to sign-only reporting and excludes fitting procedures, noise mitigation, or quantitative cross-platform comparisons. The results are supported by a publicly available, immutable hardware dataset archived on Zenodo. Related works (for reference and context): 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 — N1 (definitions and scope):https://doi.org/10.5281/zenodo.18001179 Dynamical Information Geometry (DIG) – Hardware Validation Dataset:https://doi.org/10.5281/zenodo.18099420 DIG Part IV (regime structure and operational context):https://doi.org/10.5281/zenodo.18202656 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:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work presents a strictly structural analysis of directional Twin-Sign outcomes reported in Dynamical Information Geometry (DIG) Part VII. It derives minimal response-space implications from categorical PASS/FAIL classifications under fixed audit logic, without introducing new experiments, protocols, observables, or interpretive rules. Dynamical Information Geometry assigns an effective, state-dependent information geometry to quantum many-body dynamics via the curvature of coarse-grained mutual-information profiles. Earlier work introduced the theoretical framework (Part I), provided numerical evidence for sign-sensitive refraction effects (Part II), validated a minimal operational consequence on quantum hardware (Part III), established regime structure and operational necessity (Part IV), and formulated the intrinsic multidimensional (tensorial) nature of information geometry (Part V). Subsequent work reported experimental two-dimensional Twin-Sign validation under fixed audit and regime constraints (Part VII). The present work occupies a strictly consolidating and structural position within the DIG series. It does not perform new experiments, reanalyze raw measurement data, or extend the intervention space. Instead, it analyzes what minimal response-space structure is logically implied by the directional Twin-Sign outcome patterns already reported in DIG Part VII. Specifically, the work shows that simultaneous Twin-Sign PASS outcomes along two non-collinear projection directions necessitate the existence of a multidimensional response subspace. One-dimensional Twin-Sign behavior is identified as a degenerate projection of this structure. The analysis relies solely on linear independence and audit-fixed PASS/FAIL classifications and halts explicitly prior to any geometrical, dynamical, or ontological interpretation. No claim is made regarding the full dimensionality, geometry, dynamics, or reconstructability of the underlying response space. The structural necessity identified here is consistent with the DIG No-Derivation Claim: it does not enable reconstruction, dynamical inference, or ontological identification of internal response structures. All conclusions reported in this work are fully reproducible from the categorical Twin-Sign outcomes documented in DIG Part VII, using the publicly available dataset and analysis scripts provided therein, without additional assumptions. For reference and context, related DIG manuscripts include: DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (“Positive Information Curvature and Acceleration of Operator Fronts”):https://doi.org/10.5281/zenodo.17982058 DIG Part III (“Hardware Validation of an Operational Consequence”):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (scaling 1D hardware validation):https://doi.org/10.5281/zenodo.18226369 DIG Part VII (“Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraints”):https://doi.org/10.5281/zenodo.18313460 A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179This document fixes terminology, scope, and explicit non-equivalences of the Dynamical Information Geometry framework and serves as a definitional anchor for the present work. Normative interpretation rules for the Twin Test are fixed in DIG — N2:https://doi.org/10.5281/zenodo.18380514 The DIG No-Derivation Claim and scope delimitation are documented in:https://doi.org/10.5281/zenodo.18392928 Correspondence regarding this work may be directed to:kaya@cab-film.com
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This note fixes a uniform definition of the nullspace associated with audit-fixed Twin-Test outcomes. From a finite, a priori fixed set of projection directions, it defines the realized Twin-response subspace as the span of directions passing the Twin-sign predicate, and introduces a complementary nullspace via an arbitrary non-degenerate bilinear form. The construction is purely structural: it introduces no new observables, protocols, or dynamical assumptions. A two-direction lemma clarifies when an in-plane complement exists and when any nontrivial complement must lie outside the considered two-direction plane. This work builds on: C. Kaya and D. Buck,"Dynamical Information Geometry: Microscopic Foundations of Operator Refraction",Zenodo (2025), DOI: https://doi.org/10.5281/zenodo.17966909 A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179 This document clarifies definitions, scope, and conceptual boundaries of the DIG framework. DIG — N2 (definitions/interpretation/non-equivalences) https://doi.org/10.5281/zenodo.18380514 Correspondence regarding this work may be directed to:kaya@cab-film.com note: Minor structural clarification: the complementary subspace is now defined via standard finite-dimensional direct-sum decomposition.No change to mathematical content.