The Collapse of Logical Determinism: From the Flaw in Boolos's Paradox to the Principle of Universal Structural Decay (PDSU)

This paper presents a formal deconstruction of George Boolos’s "The Hardest Logic Puzzle Ever" (1996), exposing a systematic 33.3% probability of error in the canonical resolution due to the unaddressed risk of coherent simulation by the 'Random' entity. To overcome this limitation, we introduce a three-state logic system by encoding computational deadlock (silence) as a binarizable information signal. This logical framework is then expanded into a cosmological model through the formulation of the Principle of Universal Structural Decay (PDSU), mathematically defined by the Hyperentropy equation dS(Sigma)/dt > 0. By removing the equilibrium identity (= 0) from Clausius's inequality, we postulate that absolute stability and perfect stasis are physical and logical impossibilities, providing an alternative epistemological framework for non-equilibrium states and cosmic genesis.