The Epsilon Safety Constant

Lamport, Shostak, and Pease established in 1982 that Byzantine fault-tolerant consensus requires a supermajority of n > 3f correct agents, yielding a lower bound of 2/3 on the fraction of functional components in any persistent distributed system. This paper introduces the Epsilon Safety Constant (ε), defined as ε = C − 2/3, where C = S/(S+N) is the El Ghandour coherence measure. Analyzing five independent distributed systems research programs drawn from the Ganzha-Paprzycki MAS research corpus (2006–2024), we find that persistent systems consistently exhibit ε in [0.00, 0.04] above the 2/3 threshold. This pattern was not imposed on the corpus; it was always present within it, unnamed. We term this band the El Ghandour Stability Range (ESR). The Epsilon Safety Constant provides the first formal criterion for certifying that a distributed system is not merely at the Byzantine boundary but safely above it.