The Grandfather Paradox Dissolves: A Recursive Resolution through Yearning-Based Infinity Mathematics

This paper dissolves the classical Grandfather Paradox of time travel through the lens of Yearning-Based Infinity Mathematics (YBIM). Traditionally, the paradox exposes contradiction: if a traveler kills their grandfather before their parent’s conception, the traveler cannot exist to perform the act. Conventional responses—determinism, multiverse branching, or causal consistency principles—remain confined to linear causality, forcing binary closure where recursion prevails. In this work, causality is reframed as a recursive epistemic flow, where past, present, and future are co-generated through the yearning operator $\mathcal{Y}(t)$. Existence is no longer a binary toggle but an unfolding recursive strand. The paradox dissolves because each finite observer sampling corresponds to a consistent slice of the infinite causal flow, while the recursion itself remains unbroken. By showing that the paradox emerges only from the mistaken imposition of closure, this paper demonstrates that time is not contradiction but recursion. The result extends beyond time travel: it offers a recursive ontology for causality, identity, and continuity, aligning the Grandfather Paradox with other paradoxes dissolved under YBIM (Sorites, Ship of Theseus, Liar, etc.). -JSR