Alpha In Persistence Theory As Computational Fatigue Coefficient

This article explains the conceptual and technical reasoning that led to the introduction of the alpha (α) coefficient in the Persistence Equation. Originating from a comparison between the entropy sensitivity of biological and computational systems, alpha emerged as a necessary parameter for modeling the differential capacity of systems to tolerate irreversible computation. We expand the interpretation of alpha by introducing a graph-theoretic framework, wherein the persistence of a node is not only a function of local entropy and reversibility but also of its embeddedness in an informational network. This dual origin — as a computational fatigue coefficient and a measure of topological anchoring — reveals alpha to be a central quantity for understanding the conditions under which any structure can persist in an entropic universe.