DIA-0.3: A Trace-Density Statistic for Conversational Memory Dynamics

DIA-0.3 introduces a trace-density statistic for conversational memory dynamics, formalizing the notion of effect-bearing semantic traces in dialogue. 

The framework defines trace admission via recurrence, counterfactual effect, and integration, and proposes both hard and soft gating mechanisms together with a log-multiplicative aggregation functional. It further establishes separation and degeneration properties, demonstrating when DIA provides information beyond recurrence- or topic-based measures.

Rather than claiming empirical validity, this work presents DIA as a falsifiable statistical proposal. The paper includes explicit null models and ablation criteria, and invites the research community to evaluate the framework on real conversational data.

DIA is intended as a measurable and testable construct for studying how information persists, transforms, and influences continuation in dialogue.