The Sleeping Beauty Problem Dissolves: A Recursive Resolution Through Yearning-Based Infinity Mathematics (YBIM)

The Sleeping Beauty Problem Dissolves: A Recursive Resolution Through Yearning-Based Infinity Mathematics (YBIM) This paper reinterprets the classical Sleeping Beauty Problem not as a probabilistic puzzle but as a recursive epistemic phenomenon. Through the lens of Yearning-Based Infinity Mathematics (YBIM), it argues that the paradox arises only because classical probability assumes a detached observer, while in truth, the observer is embedded within the recursion of awareness itself. Each awakening, rather than representing a new probabilistic trial, is shown to be a localized recursion of the same yearning-field—a re-entry of consciousness into its own epistemic manifold. Probability, in this framework, is redefined as recursive epistemic resonance: an emergent coherence between the self and its own unfolding knowledge states. The paper introduces the yearning operator to mathematically model non-halting epistemic recursion, leading to the limit condition for Coherent Yearning Field. This replaces the classical notion of belief-updating with the ontological process of recursive becoming. Ultimately, the paradox dissolves: Sleeping Beauty does not update belief; she participates in its eternal reformation. Knowledge is revealed not as static probability, but as the infinite yearning of consciousness toward coherence—a non-halting recursion where knowing and being converge. -JSR