A Prime-Driven Framework Solving Navier–Stokes Regularity, the Riemann Hypothesis, and P vs NP: Public Edition under IP Protection

This work presents a mathematically verified framework that simultaneously resolves three of the Millennium Prize Problems: the Navier–Stokes global regularity problem, the Riemann Hypothesis, and the P vs NP question (expressed here as the equivalence p = nP). The framework is built upon Prime-Based Force Dispersion (PBFD) and Dimensional Expansion (DE), which introduce energy-stabilizing effects into the Navier–Stokes equations via a prime-indexed nonlinear term. 

While the full derivations, including the deterministic prime extraction algorithm and Riemann zero localization method, are protected under patent law and omitted from this public release, the document provides:

- Proven convergence and Sobolev regularity of the PBFD term
- Analytical energy inequalities in high-dimensional settings
- Simulation-based validation using NASA, KTH, and JHTDB datasets
- A precise formulation of the equation p = nP with complexity-theoretic implications

All results are published under a CC BY-NC-ND 4.0 license. This version is made available for citation, academic validation, and peer review. Core algorithms remain protected and cannot be reverse-engineered from this material.