The Sixth Encompassing Dimension: A Relational-Information-Theoretic Framework for Knowledge Integration

Abstract

SEDF-1.0 — This paper introduces the Sixth Encompassing Dimension Framework (SEDF), a relational-information-theoretic framework for knowledge integration. We do not claim a new physical dimension. Instead, we formalize the sixth dimension as an emergent representational structure induced by a relational integration operator K acting on five knowledge dimensions: Spatial, Structural, Temporal, Causal, and Contextual. The framework is grounded in three pillars: (i) sufficient representation in the sense of statistical sufficiency (Y ⟂ X | K(X)), (ii) information-theoretic stability via Lipschitz continuity and Information Bottleneck, and (iii) relational topology via the complete graph K6 as a design hypothesis. We define falsifiable predictions (H1–H4) and propose an experimental program in machine learning. This version supersedes SEDF-0.7 (DOI: 10.5281/zenodo.23140509). Naming note: SEDF versions are independent of Berna AI model versions.