Relational Saturation Limit (RSL): A Regime-Dependent Theorem of Distributed Dynamical Systems

The Relational Saturation Limit (RSL) is a regime-dependent theorem: in distributed relational systems satisfying the RCR axioms A1–A5 and operating in the Active Metastability (AM) regime, centralized domination cannot achieve full-field saturation without either eliminating variance (violating Axiom A5) or sustaining continuous external energy input at cost proportional to the system's variance floor δ. This paper provides three things. First, a formal derivation of RSL from the RCR theorem chain (Theorems 0, 2, and 3 of RCR v32), making explicit the axiomatic dependencies. Second, a precise bridge between RSL and the C-A-D hierarchy decomposition: the Dominance operator D (R) = maxᵢ|Rᵢ| / (Σᵢ|Rᵢ| + ε) is analytically bounded by a ceiling determined by Cglobal dissipativity (χ), and this ceiling is the empirical correlate of the RSL saturation threshold D*. Third, a three-layer structural map of the research program and the positioning statement required for journal review. RSL makes no moral or ideological claims. It is a bounded, falsifiable structural constraint on a specific class of systems. The conditions under which it fails are as precisely stated as the conditions under which it holds.