The ρ = 1 Coordination Threshold in the General Theory of Regulated Stability Is Re-Descriptive, Not Fundamental: A Pre-Registered Negative Result

The General Theory of Regulated Stability (GTRS) is organised around a dimensionless timescale ratio ρ, with a critical value ρ = 1 proposed to separate systems that recover from a perturbation from those that do not. This note reports a pre-registered negative result. Using a structured adversarial protocol with pre-declared acceptance gates, the strongest constructive derivation of a forced coordination between three putatively independent quantities — a memory-persistence timescale, a regulatory-relaxation timescale, and a coupling/observability measure — failed a no-circularity gate, and a genericity argument shows the coordination is non-generic. We conclude that ρ = 1 is not a fundamental, substrate-general law: it is trivial near equilibrium (a linear-response artifact) and, far from equilibrium, either fine-tuned or imposed by construction. The result does not affect the separately-calibrated instrument reported in SIP-PREREG-03, is not an error correction, and is stated so as to be checkable or refutable by any reader in dynamical systems or control theory.