The Julius Crawford Paradox: A Mathematical and Philosophical Model for the Emergence of the Universe from Nothingness

This paper presents a novel theoretical framework\u2014the Julius Crawford Paradox\u2014that unifies mathematical, physical, and philosophical perspectives on the emergence of the universe from absolute nothingness. The work introduces explicit models, formalism, and conceptual insights, and is intended for interdisciplinary researchers in cosmology, philosophy of science, and mathematical physics.