MillenniumChecked

Overview

The MillenniumChecked project presents a unified constructive framework addressing the seven Millennium Prize Problems. Each problem is approached through a single harmonic and arithmetic foundation — a structural model built from the rhythm of prime numbers and their resonance patterns.

The objective is not to claim final proofs for each problem, but to present a coherent system where their underlying behaviors can be interpreted through common structural principles. Within this view, the problems share a deep connection in how numerical order, geometry, and dynamics interact under harmonic balance.

The framework extends beyond individual conjectures to illustrate how prime-based resonance may govern both discrete arithmetic systems and continuous physical fields.

Structure of the Problems

      ┌───── Birch and Swinnerton-Dyer
      ├───── Riemann Hypothesis
      ├───── Hodge Conjecture
  ┌───┴─── Based on Prime Number Structure
  │
  │   ┌───── P ≠ NP
  │   ├───── Yang–Mills Mass Gap
  │   ├───── Navier–Stokes (small data)
  │   ├───── Poincaré Conjecture
  ├───┴─── Constructive Structural Problems
  │
──┴────────────────────────────────────────
   Four Pillars of Prime Numbers
   (Elimination, Density, Resonance, Wave)