The Romero Law of Relational Stability (RZS): A Closed-Form Statement, Cross-Domain Operationalization, and Computational Verification

This paper presents the Romero Law of Relational Stability within the Relational Zero State (RZS) framework as a compact rule for comparing stability across complex systems. The law states that stability rises with effective update capacity (operational bandwidth) and falls with the combined burden of informational noise and latency. The manuscript provides clear, non-circular definitions for each term and a practical procedure for mapping them to measurable proxies in different domains, with the goal of keeping the law testable and avoiding post-hoc reinterpretation. A computational verification is reported using mean-reverting stochastic dynamics under a controlled shock window that reduces capacity while increasing noise and delay, producing the expected collapse and recovery of the stability indicator. An algebraic consistency diagnostic confirms that the stability index is computed directly from the stated relationship, without hidden fitting. The result is an operational, falsifiable stability law intended to be adaptable across fields while preserving a single core structure.