MillenniumChecked

Overview

The Millennium Prize Problems are seven of the deepest open questions in mathematics. Each has resisted resolution for decades, approached through methods native to its own domain — analytic number theory, topology, fluid dynamics, complexity theory.

This project does not claim to solve them. It exists to test something else: whether a structural paradigm with demonstrated, formally verifiable strength within number theory — and indications of reach beyond it — can withstand confrontation with problems chosen specifically because they have resisted every prior approach, each native to a domain the paradigm was not built for.

A framework broad enough to touch number theory, algebraic geometry, topology, fluid dynamics, complexity theory, and quantum field theory carries an inherent risk: that of becoming unfalsifiable, explaining everything and therefore predicting nothing. The only credible response to that risk is not to display the paradigm where it is strongest, but to submit it to trial where it is most likely to fail. These seven problems are that trial. This site does not showcase the paradigm's reach; it reports its trial by fire — what holds, and what does not, without distinction in how each is presented.

The framework developed here — built from prime number elimination cycles, harmonic interference, and relational arithmetic — offers a way to restate each problem in terms of the same underlying mechanisms. Whether this restatement brings resolution closer is an open question. What it offers is a different angle of observation.

The foundation is the Four Pillars of Prime Number Order: a constructive model in which primes arise not as atoms of multiplication, but as survivors of a deterministic elimination process — and in which the harmonic structure of that process connects naturally to questions about zeros, gaps, energy, and complexity.

This is a working research program, not a collection of finished proofs. Formal papers and preprints are available on Zenodo. The status of each problem page reflects the current depth of the structural analysis.

Structure of the Problems

      ┌───── Birch and Swinnerton-Dyer
      ├───── Riemann Hypothesis
      ├───── Hodge Conjecture
  ┌───┴─── approached via prime number structure
  │
  │   ┌───── P ≠ NP
  │   ├───── Yang–Mills Mass Gap
  │   ├───── Navier–Stokes
  │   ├───── Poincaré Conjecture
  ├───┴─── approached via constructive structural analysis
  │
──┴────────────────────────────────────────
   Four Pillars of Prime Number Order
   (Elimination, Density, Resonance, Wave)