Dynamic Geometric Modulation (DGM)

Abstract Dynamic Geometric Modulation (DGM) is a conceptual and computational protocol for conversational continuity in artificial intelligence architectures. The work proposes a two-layer architecture consisting of a theoretical-formal level, based on the notions of Background Configuration ((P_K)) and emergent relational states ((\Omega)), and an operational level that implements these hypotheses through a persistent operational state ((\Sigma)). Unlike approaches focused exclusively on conversational memory, parameter adaptation, or context retrieval, DGM explores the possibility of modulating inference through a constant-size persistent configuration that evolves across interactions. The document presents the mathematical formalization of the protocol, its reference architecture, an operational algorithm, and an experimental framework for empirical evaluation. Rather than proposing a general theory of artificial cognition, DGM formalizes an implementable and testable mechanism conceived as the computational realization of a broader theoretical framework on the relational dynamics between humans and conversational AI architectures.