Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work studies a narrowly delimited protocol-level question within an audit-fixed DIG–GIT framework: under which neutrality-preserving inference constraints is a universally admissible scalar temporal parametrization logically excluded by an observed response structure? We provide fully in-text operational definitions of direction-resolved Twin-Sign contrasts derived from raw outcome counts under a fixed evaluator. Within the specified neutrality class, we prove an existential consequence: the existence of a single audited realization with two independent direction-resolved Twin-Sign passes (dim(U)=2) excludes universal scalar temporal parametrization for that protocol/evaluator class. The claim is conditional and existential. No ontological statement about physical time is made. All quantities required for the decision rule are defined in-text. Hardware realizations and controls are documented strictly as existence witnesses. Related works:Foundations of Intervention Consistency — https://doi.org/10.5281/zenodo.18495497Definition of the Geometric Inconsistency Test (GIT) — https://doi.org/10.5281/zenodo.18499822DIG Part I — https://doi.org/10.5281/zenodo.17983399Dataset for this work — https://doi.org/10.5281/zenodo.18650719 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 studies a narrowly delimited protocol-level question within an audit-fixed DIG–GIT framework: under which neutrality-preserving inference constraints is a universally admissible scalar temporal parametrization logically excluded by an observed response structure? We provide fully in-text operational definitions of direction-resolved Twin-Sign contrasts derived from raw outcome counts under a fixed evaluator. Within the specified neutrality class, we prove an existential consequence: the existence of a single audited realization with two independent direction-resolved Twin-Sign passes (dim(U)=2) excludes universal scalar temporal parametrization for that protocol/evaluator class. The claim is conditional and existential. No ontological statement about physical time is made. All quantities required for the decision rule are defined in-text. Hardware realizations and controls are documented strictly as existence witnesses. Related works:Foundations of Intervention Consistency — https://doi.org/10.5281/zenodo.18495497Definition of the Geometric Inconsistency Test (GIT) — https://doi.org/10.5281/zenodo.18499822DIG Part I — https://doi.org/10.5281/zenodo.17983399Dataset for this work — https://doi.org/10.5281/zenodo.18650719 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.
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 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 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 manuscript establishes a minimal and audit-stable conceptual framework for reasoning about intervention consistency in experimental and protocol-level inference. It introduces precise definitions of interventions, audit-fixed evaluation rules, descriptions, consistency, and neutrality, without presupposing any physical theory, geometric structure, dimensionality, dynamics, or reconstructive ambition. The framework is intentionally non-constructive and does not introduce tests, protocols, experimental realizations, or empirical claims. Its sole purpose is to fix the logical language required to discuss consistency under interventions and to prevent hidden structural or geometric assumptions from entering subsequent analyses. In particular, the work clarifies the distinction between consistency and neutrality, and provides a terminological fixing of the term “geometric” as used in later Geometric Inconsistency Test (GIT) papers, explicitly excluding spatial, metric, or reconstructive interpretations. This paper serves as the foundational entry point (GIT 1) of the GIT series and defines the conceptual ground on which subsequent intervention-based inconsistency tests are formulated. 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 reports an experimental two-dimensional validation of the Dynamical Information Geometry (DIG) Twin-Sign protocol under fixed audit and regime constraints. Dynamical Information Geometry assigns an effective, state-dependent information geometry to quantum many-body dynamics via the curvature of a coarse-grained mutual-information profile. 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 tensorial nature of information curvature in dimensions greater than one (Part V). The present work occupies a strictly operational and consolidating role within the DIG series. It does not introduce new theoretical postulates, derivations, observables, or interpretive claims. Instead, it tests whether the multidimensional, projection-based structure articulated in DIG Part V remains internally consistent when subjected to the mandatory audit logic and regime language fixed in DIG Part IV. Twin-Sign tests are performed in two spatial dimensions along two non-collinear directions, without privileging any spatial axis. All results are derived exclusively from raw measurement counts under fixed audit invariants. No readout mitigation, post-selection, fitting procedures, or cross-platform normalization is applied. In addition to positive validation runs, the dataset includes a structurally defined negative control (One-Sided Twin), which is shown to fail deterministically. Across sampled values of the lens-strength protocol parameter, the observed outcomes recover the finite onset–window–breakdown regime structure introduced in DIG Part IV. This behavior is reported descriptively, without invoking universality, sharp thresholds, or new scaling claims. The results demonstrate that the operational and structural content consolidated in DIG Part IV persists under the multidimensional extension of the framework. Directional asymmetries and null projections are observed and are consistent with the tensorial formulation of information geometry in dimensions greater than one. All results reported in this work are fully reproducible from the accompanying public dataset without additional assumptions. Related DIG materials 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 V (multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (dataset):https://doi.org/10.5281/zenodo.18226272 DIG Part VII (dataset):Dataset for Experimental Validation of Dynamical Information Geometry in Two Dimensionshttps://doi.org/10.5281/zenodo.18309526 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 - Correspondence regarding this work may be directed to:kaya@cab-film.com