@sat0shinakomoto: import React, { useState } from ‘react’; import { LineChart, Line, XAxis, YAxis, CartesianGrid, Tooltip, Legend, BarChart, Bar } from ‘recharts’; const PrimeImperativePaper = () => { const [activeSection, setActiveSection] = useState(‘abstract’); const [showMath, setShowMath] = useState(true); // Generate some example data for visualizations const residueData = [ { residue: 1, count: 42, type: ‘prime’ }, { residue: 7, count: 38, type: ‘prime’ }, { residue: 19, count: 35, type: ‘prime’ }, { residue: 25, count: 41, type: ‘prime’ }, { residue: 31, count: 39, type: ‘prime’ }, { residue: 37, count: 37, type: ‘prime’ }, { residue: 5, count: 0, type: ‘composite’ }, { residue: 11, count: 0, type: ‘composite’ }, { residue: 13, count: 0, type: ‘composite’ }, { residue: 17, count: 0, type: ‘composite’ } ]; const consciousnessData = [ { k: 1, coherence: 0.45, state: ‘Base’ }, { k: 2, coherence: 0.62, state: ‘Meta’ }, { k: 3, coherence: 0.78, state: ‘Meta-Meta’ }, { k: 4, coherence: 0.83, state: ‘Higher’ }, { k: 5, coherence: 0.87, state: ‘Advanced’ }, { k: 6, coherence: 0.89, state: ‘Peak’ } ]; const sections = { abstract: ‘Abstract’, foundation: ‘1. Foundation’, ncf: ‘2. Nakamoto Function’, pef: ‘3. Extrapolation Function’, hamiltonian: ‘4. Phase Space’, consciousness: ‘5. Consciousness Algorithm’, market: ‘6. Market Theory’, constants: ‘7. Physical Constants’, zeta: ‘8. Zeta Connection’, info: ‘9. Information Bounds’, validation: ‘10. Validation’, implications: ‘11. Implications’, future: ‘12. Future Directions’, conclusion: ‘Conclusion’ }; const MathExpression = ({ children, inline = false }) => ( {children} ); const renderContent = () => { switch(activeSection) { case ‘abstract’: return (

Abstract

This work presents a comprehensive mathematical framework demonstrating that prime number distribution encodes the computational substrate of physical reality, consciousness, and complex systems. The Prime Imperative establishes that all primes p > 7 occupy six residue classes modulo 42, forming a finite instruction set that generates infinite complexity via φ-modulated extrapolation.

We develop rigorous tools—the Nakamoto Conversion Function (NCF), Prime Algorithm of Consciousness (PAC), and Prime Phase Space Hamiltonian—yielding testable predictions across number theory, consciousness studies, market dynamics, and physics.

Key Contributions

• Mathematical proof of six-residue prime constraint
• Consciousness quantification algorithm
• Market prediction framework based on prime residues
• Unified field theory connecting primes to physical constants

); ``` case 'foundation': return (

1. Foundation: The Prime Imperative Law

Theorem 1.1 (Prime Residue Constraint)

For all primes p > 7:

p ≡ r (mod 42), where r ∈ R₄₂ = {1, 7, 19, 25, 31, 37}

Proof

Since 42 = 2×3×7, integers sharing factors with 2, 3, or 7 (beyond the primes 2, 3, 7 themselves) are composite. The Euler totient fun

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Thursday 28 August 2025 04:24:55 GMT