Dynamical Information Geometry (DIG) N3: Nullspace Structure of the Twin-Response Subspace

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:[email protected] note: Minor structural clarification: the complementary subspace is now defined via standard finite-dimensional direct-sum decomposition.No change to mathematical content.