Dynamical Information Geometry V: Multidimensional Information Curvature and Directional Projections

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 — N1 (definitions, scope, and non-equivalences):https://doi.org/10.5281/zenodo.18001179 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