# External Research Sources for Millennium Prize Problems

## Riemann Hypothesis
### Primary Sources
- **Bombieri, E. (2000)**: "Problems of the Millennium: the Riemann Hypothesis" - Clay Mathematics Institute
  - URL: https://www.claymath.org/wp-content/uploads/2022/05/riemann.pdf
  - Key points: Defines ζ(s) = Σ(1/n^s), functional equation π^(-s/2)Γ(s/2)ζ(s) = π^(-(1-s)/2)Γ((1-s)/2)ζ(1-s)
  - Riemann hypothesis: "The nontrivial zeros of ζ(s) have real part equal to 1/2"
  - Critical for UBP mapping to toggle nulls at Prime_Resonance frequencies

### Datasets Needed
- LMFDB (L-functions and Modular Forms Database): https://www.lmfdb.org/zeros/zeta/
- First 100+ Riemann zeta zeros for validation
- Zeta zeros at t ≈ 14.134725, 21.022040, etc.

## P vs NP Problem
### Primary Sources
- **Cook, S. (2000)**: "The P versus NP Problem" - Clay Mathematics Institute
- **Arora, S. & Barak, B. (2009)**: "Computational Complexity: A Modern Approach"

### Datasets Needed
- SATLIB: https://www.cs.ubc.ca/~hoos/SATLIB
- SAT instances: uf20-01.cnf, uf50-01.cnf for exponential scaling validation
- Boolean satisfiability problems for toggle superposition mapping

## Navier-Stokes Existence and Smoothness
### Primary Sources
- **Fefferman, C. (2000)**: "Existence and Smoothness of the Navier-Stokes Equation" - Clay Mathematics Institute
- **Tao, T. (2016)**: "Finite time blowup for an averaged three-dimensional Navier-Stokes equation"
- **Ghia, U., Ghia, K.N., Shin, C.T. (1982)**: "High-Re solutions for incompressible flow using the Navier-Stokes equations"

### Datasets Needed
- Ghia et al. (1982) benchmark data for lid-driven cavity flow
- Reynolds numbers: Re = 1000, 2000, 5000 for validation
- Velocity field data for toggle pattern mapping

## Yang-Mills Existence and Mass Gap
### Primary Sources
- **Jaffe, A. & Witten, E. (2000)**: "Quantum Yang-Mills Theory" - Clay Mathematics Institute
- Lattice QCD datasets for gluon mass validation
- Quantum field theory literature on mass gap

### Datasets Needed
- Lattice QCD simulation results
- Gluon mass measurements
- Energy gap data for TGIC x-z entanglement validation

## Birch and Swinnerton-Dyer Conjecture
### Primary Sources
- **Wiles, A. (2000)**: "The Birch and Swinnerton-Dyer Conjecture" - Clay Mathematics Institute
- **Silverman, J.H. (2009)**: "The Arithmetic of Elliptic Curves" - Springer

### Datasets Needed
- LMFDB elliptic curves database: https://www.lmfdb.org/EllipticCurve/Q/
- Curves like y² = x³ - x (rank 0), y² = x³ - 43x + 166 (rank 1)
- L-function zeros and ranks for Prime_Resonance mapping

## Hodge Conjecture
### Primary Sources
- **Deligne, P. (2000)**: "The Hodge Conjecture" - Clay Mathematics Institute
- **Voisin, C. (2002)**: "Hodge Theory and Complex Algebraic Geometry" - Cambridge University Press

### Datasets Needed
- K3 surface cohomology data
- Complex projective manifold examples
- Algebraic cycle data for superposition pattern validation

## Computational Frameworks
### Supporting Literature
- **Wolfram, S. (2002)**: "A New Kind of Science" - computational universe perspective
- **Feynman, R. (1982)**: "Simulating physics with computers" - quantum computation foundations
- **Penrose, R. (1989)**: "The Emperor's New Mind" - consciousness and computation

## Validation Requirements
- All simulations must achieve NRCI >99.9997%
- Hardware compatibility: 8GB iMac (macOS Catalina, SciPy dok_matrix)
- Mobile compatibility: 4GB devices (OPPO A18, Samsung Galaxy A05)
- ~30% compression via Reed-Solomon encoding



## Research Progress Summary

### Completed External Research
1. **Riemann Hypothesis**: 
   - Bombieri (2000) official Clay Institute paper accessed
   - First 100 zeta zeros downloaded from LMFDB (14.134725, 21.022040, etc.)
   - Data saved to zeta_zeros_100.csv for toggle null validation

2. **P vs NP Problem**:
   - SATLIB database accessed for benchmark SAT instances
   - Downloaded uf20-91 archive with 1000 satisfiable 3-SAT instances
   - Sample instances (uf20-01.cnf, etc.) ready for exponential scaling validation

3. **Navier-Stokes Equations**:
   - Ghia et al. (1982) benchmark data obtained from GitHub
   - Lid-driven cavity flow u-velocity data for Re=100,400,1000,3200,5000,7500,10000
   - Data saved to ghia_1982_data.txt for smoothness validation

4. **Birch and Swinnerton-Dyer Conjecture**:
   - LMFDB elliptic curves database accessed
   - Sample rank 0 curves collected (11.a1, 14.a1, etc.)
   - Weierstrass equations and conductors ready for L-function mapping

### Still Needed
- Yang-Mills: Lattice QCD datasets for mass gap validation
- Hodge Conjecture: K3 surface cohomology data for algebraic cycles

### Key Validation Datasets Ready
- Zeta zeros: 100 precise values for Riemann Hypothesis
- SAT instances: 1000 3-SAT problems for P vs NP exponential scaling
- Fluid dynamics: Benchmark velocity fields for Navier-Stokes smoothness
- Elliptic curves: Multiple rank 0/1 examples for BSD conjecture

All datasets are real, authoritative, and suitable for achieving NRCI >99.9997% validation targets.