Invariant-Admissible Resolution Dynamics (IARD) Formal Closure of Self-Rewriting Agents Under the Relative Framework

This paper completes the formal architecture of the RCN by resolving the final open degree of freedom in resolution-based self-rewriting agents: the admissible class of internal transformations. While prior work established Resolution as the objective function and Invariant-Bounded Resolution (IBR) as the halting condition, the rewrite dynamics themselves remained intentionally under-specified. Invariant-Admissible Resolution Dynamics (IARD) formally closes this gap by defining the necessary and sufficient constraints under which recursive self-modification preserves identity invariants, prevents oscillatory collapse, and converges or plateaus coherently under irreducible conflict. No new axioms, goals, or architectural components are introduced. This work finalizes the RCN as a closed, instantiable system grounded in epistemic humility, relational ontology, and non-coercive alignment. ORCID: 0009-0006-6041-352XWeb of Science ResearcherID: OYD-9537-2025