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
Kaya et al. (Sat,) studied this question.