SIP-CORE-03 v2.0 GTRS Foundations: First Principles of Regulated Stability The governing architecture of the Sovereign Ideas Papers corpus

Abstract The General Theory of Regulated Stability (GTRS) proposes that all persistent complex systems — biological, cognitive, social, ecological, and artificial — share a common regulatory grammar. This paper defines that grammar from first principles. The core construct is the regulatory ratio ρ = R/σ, where R denotes the system’s regulatory capacity and σ the stressor load it faces. Coherence is the system-level consequence of sustained ρ > 1; decoherence is the trajectory when ρ declines toward unity. The Coherence–Decoherence–Recoherence (CDR) cycle formalises the universal phase grammar through which systems maintain, lose, and recover structural integrity. The α < 1 principle — where α := inf{ρ : system can sustain coherence indefinitely} — asserts that no persistent system can occupy the symmetric vacuum (ρ = 0, σ = 0); existence is regulation. Four falsification criteria are specified. GTRS claims structural isomorphism across domains, not ontological reduction: the same phase grammar generates testable predictions whether applied to neural coherence, ecological succession, AI memory governance, or lattice gauge theory. This document serves as the anchor for the SIP corpus; all applied papers cite it for foundational definitions. Keywords: regulated stability, coherence, decoherence, recoherence, homeostasis, attractor dynamics, phase transitions, cross-domain theory, falsification, sovereign research