Extended Proofs for the Unified Resolution of the Millennium Problems via the Tenson Theory: A Complex Tensor Approach to Mathematical Reality

This extended version deepens the mathematical treatment of the Millennium Problems under the Tenson Theory. We derive each problem as a special solution of the complex tensor conservation law: ∇µT µν = 0, Tµν = Eµν + iIµν, where Eµν denotes measurable energy curvature and Iµν the informational potential. Each classical conjecture emerges as a condition of tensor smoothness, closure, or resonance. This paper expands on the proof sketches, showing how existing analytic formulations appear as projections of the same information–energy symmetry.