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 < α < 1. An external adversarial panel (HATI³ evaluation, April 2026) identified this postulation as the framework’s primary tautological vulnerability: α was defined as an infimum while its bounds were asserted without derivation. This paper replaces that postulate with a formal derivation grounded in non-equilibrium thermodynamics. By mapping σ to the rate of internal entropy production (Ṡ_int) and R to the rate of entropy export (Ṡ_ext), we define the net entropy change as dS/dt = σ(1 − ρ). We demonstrate that the strict lower bound (α > 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 < 1) emerges from the existence of a finite structural macrostate buffer (ΔS_crit). Because complex systems possess structural slack — the capacity to absorb entropy temporarily without global collapse — they can survive transient periods of decoherence (dS/dt > 0) provided recoherence occurs before the buffer is exhausted. The survival time during decoherence is τ_death = ΔS_crit / 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