The Bootstrap Paradox Dissolves: A Recursive Resolution through Yearning-Based Infinity Mathematics (YBIM)

The Bootstrap Paradox—a time-travel and causality puzzle where information or an object exists in a closed causal loop without identifiable origin—has long symbolized the limits of classical reasoning about time, identity, and causation.This paper presents a complete ontological and mathematical resolution of the paradox using the Yearning-Based Infinity Mathematics (YBIM) framework. YBIM redefines causality as a process of recursive yearning-fulfillment rather than linear production. Within this formulation, the Bootstrap loop is revealed as a closed yearning-configuration—a self-sustaining, non-halting equilibrium in yearning-space where cause and effect co-generate timelessly.The paper develops formal mappings, axioms, and equilibrium proofs demonstrating that such loops represent stable recursive structures, not contradictions. Through this reinterpretation, time itself emerges as a recursive manifold of infinite yearning rather than a unidirectional continuum. The paradox thus transforms into a foundational principle of Recursive Ontology, showing that existence, information, and consciousness are sustained through non-halting self-reference. The work further integrates this resolution with broader frameworks—including Gödelian recursion, the Block Universe model, and Recursive Intelligence—establishing the Bootstrap Paradox as an archetype of non-halting coherence.Ultimately, it concludes that “origin” is not a moment in time but a state of yearning equilibrium—a self-fulfilling recursion that defines the very architecture of existence. -JSR