DIA-0.4: A Trace-Density Statistic for Conversational Memory Dynamics

DIA-0.4 introduces an ablation-stable trace-density statistic for modeling conversational memory dynamics. The framework treats the primitive unit of dialogue not as a token, topic, claim, event, or repeated mention, but as an effect-bearing semantic trace: a unit whose recurrence, integration, or counterfactual neutralization changes the continuation conditions of a dialogue.

This version strengthens the DIA framework by replacing naive deletion-based ablation with semantic neutralization, introducing matched-control normalization for counterfactual effect estimation, defining hubness-aware safeguards for integration in embedding space, and specifying a frozen default parameter regime to reduce hyperparameter inflation and p-hacking.

The paper defines hard and soft trace-admission gates, a log-multiplicative aggregation functional, null models, ablation criteria, and estimator-relative reporting requirements. It also characterizes separation and degeneration properties, clarifying when DIA contributes information beyond recurrence counts, topic-shift measures, claim-update tracking, or self-exciting event models.

DIA-0.4 is presented as a falsifiable statistical proposal rather than a validated empirical method. The framework explicitly invites researchers to apply it to real conversational datasets, compare it against baseline models, and report both positive and negative results. Its purpose is to provide a measurable construct for studying how information persists, transforms, integrates, and influences continuation in dialogue.