The Active Geometric Resonance Hypothesis: A Theoretical Framework for Information Persistence During Biological Remodeling

The Active Geometric Resonance Hypothesis: A Theoretical Framework for Information Persistence During Biological Remodeling This manuscript presents the Active Geometric Resonance Hypothesis (AGRH), a theoretical framework proposing that biological information may remain continuous during large-scale structural remodeling through the interaction of evolving geometry, bioelectric dynamics, and active biological feedback. Using insect metamorphosis as the primary biological test case, the hypothesis explores how information-bearing states may persist despite extensive material turnover. The manuscript develops a mathematical framework based on evolving bounded domains, coupled electro-diffusive dynamics, geometry-dependent spatial modes, and information theory. It introduces explicit axioms, a mathematical identity, a physical model, competing mechanistic explanations, and experimentally falsifiable predictions designed to distinguish the proposed mechanism from traditional connectionist and purely molecular models. Although motivated by memory persistence across metamorphosis, the framework is generalized to broader developmental processes including regeneration, embryogenesis, wound healing, and organ remodeling. This work is presented as a testable theoretical hypothesis intended to generate experimentally verifiable predictions rather than describe an established biological mechanism.