Relational Saturation Limit (RSL): A Regime-Dependent Theorem of Distributed Dynamical Systems
Year: 2026
Type: article
Abstract: 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 C_global 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.
Author: Gallant, Justin D
Institution: Institute for Doctoral Studies in the Visual Arts
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161564774
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