This paper introduces Crystallization Theory, a framework for knowledge validation in multi-contributor AI memory systems. Drawing from Hebbian learning principles in neuroscience, the framework proposes that shared knowledge "crystallizes" through repeated confirmation across multiple contributors, while unconfirmed or contradicted information naturally decays. The paper presents three interconnected components: (1) Crystallization Theory itself—a model for how knowledge emerges and solidifies through multi-source validation, (2) Communal Inference Reinforcement (CIR)—a training paradigm that rewards inference from sparse shared signals, and (3) a Core Memory Architecture separating AI-discovered patterns from human-provided context. Keywords: AI memory architecture, multi-agent systems, federated learning, Hebbian learning, RAG, knowledge validation