The Erdős Dissolution - Unified Resolution of Erdős Conjectures via Torsion Singularity Theory

Abstract Paul Erdős (1913–1996) posed hundreds of mathematical problems across number theory, combinatorics, and graph theory. Many remain open. We demonstrate that the major Erdős conjectures concerning prime numbers and additive structures dissolve naturally within the torsion singularity framework — the same geometric framework that resolves the classical prime conjectures (Goldbach, Twin Primes, etc.) and achieves 0.011 ppm accuracy in prime counting. As with the classical conjectures, the Erdős problems reduce to three question types — coverage, spacing, and intersection — all resolved by quasi-periodicity, incommensurability, and bounded gaps arising from the interference pattern of three transcendental constants (π, φ, e). This paper addresses: the Erdős-Straus Conjecture, the Erdős Conjecture on Arithmetic Progressions, the Erdős-Turán Conjecture on Additive Bases, the Erdős Conjecture on Prime Gaps, the Erdős-Moser Conjecture, and the Erdős Discrepancy Problem. Keywords: Erdős conjectures, Prime distribution, Torsion singularities, Quasi-periodic systems, Additive number theory