PFUSRC-152 Topological Reassignment of the Seven Millennium Prize Problems ——Seven Manifestations of a Single Paradigm Predicament

The seven Millennium Prize Problems, including the smoothness of the Navier-Stokes equations, P vs NP, the Poincaré conjecture, the Riemann hypothesis, the Yang-Mills mass gap, the BSD conjecture and the Hodge conjecture, are recognized as the hardest open mathematical problems. Only the Poincaré conjecture has been proven to date. This paper puts forward a unified core judgment: the seven problems are seven different manifestations of one single paradigm predicament. They share three implicit presuppositions: three-dimensional homogeneous continuous space, reductionist methodology and single-point deterministic truth. All answers lie outside these presuppositions. Based on the core frameworks of PFUSRC system including primordial steady-state bicone topology, logical origin theory and living calculus, this paper carries out topological reassignment for each problem respectively. This paper distinguishes clearly between "reassignment" and rigorous mathematical proof: reassignment locates each problem at the correct hierarchical level and provides general research direction, while detailed mathematical derivation needs to be completed in follow-up specialized papers. The core verdict is that the seven puzzles stem from the limitation of mainstream research paradigms rather than technical obstacles; once the PFUSRC hierarchical ontology framework is adopted, all seven problems can be simultaneously positioned and clarified.