The Topologies of Incompleteness: A Relational Resolution to the Millennium Prize Problems

This paper applies the Oros Fundus operator-algebraic framework (DOI: 10.5281/zenodo.19599247) to demonstrate that the six unresolved Millennium Prize Problems are six distinct manifestations of the identical topological boundary condition — the point where continuous associative geometry meets the discrete non-associative exceptional boundary of the Type III₁ von Neumann algebra framework. Problems addressed: Yang-Mills Mass Gap, Navier-Stokes Smoothness and Blowup, P vs NP, the Riemann Hypothesis, the Hodge Conjecture, and Birch and Swinnerton-Dyer Conjecture. The arguments are structural and operator-algebraic in nature. This is a preliminary version establishing structural priority. Expanded proofs will follow in subsequent work. Companion paper (foundational framework): Oros Fundus: A Relational Unification Framework via Type III₁ AlgebrasDOI: 10.5281/zenodo.19599247