How Causally Useful Information Becomes Cumulative: A Criterion-Indexed Framework for Retention, Transfer, and Reusable Hierarchy in Adaptive Systems

Intervention-based approaches distinguish statistical correlation from information that causally changes a system's future under a declared outcome criterion. HSRR addresses the subsequent transition: when does a causally useful relation persist, survive relevant change, and become a reusable building block that reduces later adaptation cost? The core profile contains causal contribution C, signed retention H, eligibility-gated transfer G, and reuse R=(B,S,L). G is defined only when baseline C is reliably positive above a preregistered smallest effect of interest; otherwise G is NA rather than zero, and baseline-harmful relations are analysed separately. Counterfactual reach is optional. The critical test asks whether H, eligible G, and R predict adaptation in held-out environment families beyond current C, mutual information, reward, memory, model size, and compute. A capacity-matched artificial-agent protocol is proposed. Version 1.3 of the HSRR theoretical framework. This record contains the English hypothesis paper and its prospective Study 1 protocol. No empirical results are included, and Study 1 has not yet been preregistered. ChatGPT (OpenAI) and Claude (Anthropic) assisted with specified preparation tasks; the author reviewed and edited the content, verified cited sources, and takes full responsibility.