SIP-CORE-04 v1.0 The Thermodynamic Bounds of Regulated Stability Deriving 0 < α < 1 from Non-Equilibrium Entropy Balanc

The General Theory of Regulated Stability (GTRS) posits that the persistence of complex systems is governed by the regulatory ratio ρ = R/σ, where R is regulatory capacity and σ is perturbation pressure. In the foundational architecture (SIP-CORE-03, DOI: 10. 5281/zenodo. 19588952), the lower bound of sustainable existence — the infimum α — was postulated to satisfy 0 0) is an obligate consequence of the Second Law of Thermodynamics: no system can survive the symmetric vacuum without active regulatory work. Furthermore, we prove that the upper bound (α 0) provided recoherence occurs before the buffer is exhausted. The survival time during decoherence is τdeath = ΔScrit / σ (1 − ρ), establishing a quantitative link between thermodynamic buffer depth and CDR dynamics. By deriving these bounds from physical law rather than asserting them from observation, this paper establishes GTRS not merely as a qualitative taxonomy but as a thermodynamically grounded theory of complex system survival. The multi-buffer nested hierarchy is introduced to explain the Captured Recoherence State (CRS) as a system operating on a secondary, shallower entropy buffer after exhaustion of its primary buffer. Keywords: non-equilibrium thermodynamics, entropy production, macrostate buffer, regulatory ratio, dissipative structures, GTRS, phase transitions, Captured Recoherence State, complex systems, Second Law