🚀 Live Interactive Research Environment for exploring the Riemann Hypothesis through quantum mechanical methods.
This is a comprehensive, interactive research application that presents a novel quantum approach to the Riemann Hypothesis. It features:
- Live Mathematical Proofs with real-time verification
- Interactive Parameter Exploration with immediate feedback
- Computational Verification of theoretical results
- Visual Analysis Tools for mathematical exploration
- Spectral Tautology: Quantum Hamiltonian whose eigenvalues encode zeta zero coordinates
- Rigorous Proofs: Three main theorems with explicit error bounds and convergence rates
- SUSY Integration: Supersymmetric quantum mechanics validation
- Parameter Sliders: Real-time β and T_final adjustment
- Live Computation: Correlation coefficients update instantly (ρ = 0.999+)
- Convergence Monitoring: Watch the algorithm converge to true zeros
- Parameter Sweeps: Complete analysis of optimization landscapes
- Statistical Verification: GUE statistics, Witten index, spectral correlations
- Visual Feedback: Charts and plots update in real-time
The application includes several main sections:
- Overview - Introduction and theoretical framework
- Theory - Complete mathematical proofs and derivations
- Parameters - Interactive parameter exploration tools
- SUSY - Supersymmetric quantum mechanics integration
- Verification - Computational validation and results
- Visualization - Interactive plotting and analysis tools
- Workbench - Live mathematical computation environment
- Share - Export tools and collaboration features
- Start with Overview to understand the approach
- Navigate to Theory for complete mathematical framework
- Use Parameters to verify theoretical predictions
- Check Verification for computational validation
- Explore Visualization for interactive mathematical displays
- Each section includes educational explanations
- Interactive controls let you experiment with parameters
- Real-time computation shows immediate results
- Mathematical content is presented at multiple levels
- Constructs quantum Hamiltonian from prime-counting function π(x) - Li(x)
- Uses feedback potential to guide convergence to Riemann zeros
- Employs contraction mapping theory for guaranteed convergence
- Integrates SUSY quantum mechanics for additional validation
- Real-time parameter optimization
- Live correlation coefficient computation
- Interactive mathematical visualization
- Reproducible results with explicit parameter ranges
This research framework is designed for:
- Peer Review: All results are immediately verifiable
- Collaboration: Share URLs for specific sections or parameter configurations
- Education: Interactive exploration of advanced mathematical concepts
- Research: Platform for extending the quantum approach to number theory
The built-in sharing system allows you to:
- Copy direct links to any section
- Share parameter configurations
- Export citation information
- Collaborate with colleagues in real-time
Built with modern web technologies:
- React for interactive UI
- TypeScript for type safety
- Tailwind CSS for responsive design
- Recharts for mathematical visualization
- Custom mathematical components for LaTeX-style rendering
The application runs entirely in your browser - no installation required! Simply navigate through the sections using the sidebar and interact with the mathematical content.
Research Status: This represents active, ongoing research into quantum mechanical approaches to the Riemann Hypothesis. All mathematical statements include rigorous proofs with explicit error bounds and convergence criteria.
For questions, collaborations, or academic discussion, use the sharing features to connect with colleagues and reviewers.