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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>SRC Algorithm Visualizer</title>
<script src="https://cdn.tailwindcss.com"></script>
<script src="https://unpkg.com/feather-icons"></script>
<script src="https://cdn.jsdelivr.net/npm/feather-icons/dist/feather.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js"></script>
<style>
body {
background: linear-gradient(135deg, #0f172a, #1e293b);
color: #f1f5f9;
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
}
.hilbert-space {
background: rgba(15, 23, 42, 0.7);
border: 1px solid #334155;
box-shadow: 0 0 20px rgba(99, 102, 241, 0.2);
}
.prime-state {
transition: all 0.5s ease;
}
.active-state {
box-shadow: 0 0 15px #818cf8;
transform: scale(1.1);
}
.resonance-path {
stroke-dasharray: 1000;
stroke-dashoffset: 1000;
}
.entropy-graph {
background: rgba(30, 41, 59, 0.8);
}
.control-panel {
background: rgba(15, 23, 42, 0.9);
backdrop-filter: blur(10px);
}
.algorithm-step {
transition: all 0.3s ease;
}
.current-step {
background: rgba(99, 102, 241, 0.2);
border-left: 3px solid #818cf8;
}
</style>
</head>
<body class="min-h-screen">
<!-- Header -->
<header class="py-6 px-4 sm:px-6 lg:px-8 border-b border-slate-700">
<div class="max-w-7xl mx-auto flex flex-col md:flex-row justify-between items-center">
<div>
<h1 class="text-3xl font-bold text-indigo-300">Symbolic Resonance Collapse</h1>
<p class="text-slate-400 mt-1">Visualization of P = NP Proof</p>
</div>
<div class="mt-4 md:mt-0 flex items-center space-x-4">
<div class="bg-indigo-900/30 px-4 py-2 rounded-lg">
<span class="text-indigo-300 font-mono">P = NP</span>
</div>
<div class="text-sm text-slate-400">
Sebastian Schepis, 2025
</div>
</div>
</div>
</header>
<!-- Main Content -->
<main class="max-w-7xl mx-auto py-8 px-4 sm:px-6 lg:px-8">
<div class="grid grid-cols-1 lg:grid-cols-3 gap-8">
<!-- Visualization Panel -->
<div class="lg:col-span-2">
<div class="hilbert-space rounded-xl p-6">
<div class="flex justify-between items-center mb-6">
<h2 class="text-xl font-semibold text-indigo-200">Prime-Encoded Hilbert Space</h2>
<div class="flex space-x-2">
<button id="resetBtn" class="px-3 py-1 bg-slate-700 hover:bg-slate-600 rounded-lg text-sm">
Reset
</button>
<button id="startBtn" class="px-3 py-1 bg-indigo-600 hover:bg-indigo-500 rounded-lg text-sm">
Start Simulation
</button>
</div>
</div>
<!-- Hilbert Space Visualization -->
<div class="relative h-96 rounded-lg border border-slate-600 bg-slate-900/50 overflow-hidden">
<div id="hilbertCanvas" class="w-full h-full relative">
<!-- Prime states will be dynamically added here -->
</div>
<!-- Resonance path -->
<svg class="absolute top-0 left-0 w-full h-full pointer-events-none">
<path id="resonancePath" class="resonance-path" fill="none" stroke="#818cf8" stroke-width="2"></path>
</svg>
</div>
<!-- System Status -->
<div class="mt-6 grid grid-cols-1 md:grid-cols-3 gap-4">
<div class="bg-slate-800/50 p-4 rounded-lg">
<div class="text-sm text-slate-400">Current State</div>
<div id="currentState" class="text-lg font-mono text-indigo-300">|Ψ₀⟩</div>
</div>
<div class="bg-slate-800/50 p-4 rounded-lg">
<div class="text-sm text-slate-400">Entropy</div>
<div id="entropyValue" class="text-lg font-mono text-green-300">S₀</div>
</div>
<div class="bg-slate-800/50 p-4 rounded-lg">
<div class="text-sm text-slate-400">Time Step</div>
<div id="timeStep" class="text-lg font-mono text-yellow-300">t = 0</div>
</div>
</div>
</div>
<!-- Entropy Graph -->
<div class="hilbert-space rounded-xl p-6 mt-8">
<h2 class="text-xl font-semibold text-indigo-200 mb-4">Entropy Convergence</h2>
<div class="entropy-graph rounded-lg p-4 h-64">
<canvas id="entropyChart" width="800" height="200"></canvas>
</div>
</div>
</div>
<!-- Control Panel -->
<div class="control-panel rounded-xl p-6 h-fit">
<h2 class="text-xl font-semibold text-indigo-200 mb-4">Algorithm Steps</h2>
<div class="space-y-4">
<div class="algorithm-step p-4 rounded-lg current-step" data-step="0">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-indigo-500 flex items-center justify-center text-xs font-bold">1</div>
<div class="ml-3">
<h3 class="font-medium text-white">Prime-Encoded Hilbert Space</h3>
<p class="mt-1 text-sm text-slate-400">Define HP over prime-number eigenstates |p⟩ for Boolean variables</p>
</div>
</div>
</div>
<div class="algorithm-step p-4 rounded-lg" data-step="1">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">2</div>
<div class="ml-3">
<h3 class="font-medium text-white">SAT Representation</h3>
<p class="mt-1 text-sm text-slate-400">Encode SAT instance Φ into symbolic state |Ψ₀⟩ ∈ H⊗nP</p>
</div>
</div>
</div>
<div class="algorithm-step p-4 rounded-lg" data-step="2">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">3</div>
<div class="ml-3">
<h3 class="font-medium text-white">Symbolic Operators</h3>
<p class="mt-1 text-sm text-slate-400">Define Hamiltonian ĤΦ and Resonance Operator R̂</p>
</div>
</div>
</div>
<div class="algorithm-step p-4 rounded-lg" data-step="3">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">4</div>
<div class="ml-3">
<h3 class="font-medium text-white">System Evolution</h3>
<p class="mt-1 text-sm text-slate-400">Evolve |Ψ(t)⟩ using symbolic Schrödinger equation</p>
</div>
</div>
</div>
<div class="algorithm-step p-4 rounded-lg" data-step="4">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">5</div>
<div class="ml-3">
<h3 class="font-medium text-white">Entropy Minimization</h3>
<p class="mt-1 text-sm text-slate-400">S(t) decreases as system approaches stable state</p>
</div>
</div>
</div>
<div class="algorithm-step p-4 rounded-lg" data-step="5">
<div class="flex items-start">
<div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">6</div>
<div class="ml-3">
<h3 class="font-medium text-white">Polynomial Convergence</h3>
<p class="mt-1 text-sm text-slate-400">System reaches |Ψ*⟩ in O(nᵏ) symbolic time</p>
</div>
</div>
</div>
</div>
<!-- Parameters -->
<div class="mt-8">
<h3 class="font-medium text-white mb-3">Simulation Parameters</h3>
<div class="space-y-4">
<div>
<label class="block text-sm text-slate-400 mb-1">Variables (n)</label>
<input type="range" min="3" max="10" value="5" id="varCount" class="w-full">
<div class="text-right text-sm text-slate-400" id="varCountValue">5</div>
</div>
<div>
<label class="block text-sm text-slate-400 mb-1">Clauses (m)</label>
<input type="range" min="3" max="15" value="7" id="clauseCount" class="w-full">
<div class="text-right text-sm text-slate-400" id="clauseCountValue">7</div>
</div>
<div>
<label class="block text-sm text-slate-400 mb-1">Decay Constant (λ)</label>
<input type="range" min="0.1" max="2" step="0.1" value="0.5" id="decayConstant" class="w-full">
<div class="text-right text-sm text-slate-400" id="decayValue">0.5</div>
</div>
</div>
</div>
</div>
</div>
<!-- Explanation Section -->
<div class="mt-12 hilbert-space rounded-xl p-8">
<h2 class="text-2xl font-bold text-indigo-200 mb-6">How Symbolic Resonance Collapse Works</h2>
<div class="grid grid-cols-1 md:grid-cols-2 gap-8">
<div>
<h3 class="text-lg font-semibold text-white mb-3">The Framework</h3>
<p class="text-slate-300 mb-4">
The SRC framework redefines computation as an entropic resonance process in a quantum-inspired
Hilbert space over prime-number eigenstates. Instead of combinatorial search, NP-complete problems
converge to solution states through entropy-driven alignment.
</p>
<p class="text-slate-300">
SAT instances are modeled as symbolic wavefunctions undergoing entropy minimization, with clause
interactions acting as quantum-like operators in a resonance field.
</p>
</div>
<div>
<h3 class="text-lg font-semibold text-white mb-3">Key Insights</h3>
<ul class="space-y-2 text-slate-300">
<li class="flex items-start">
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
<span>Computation as coherence alignment rather than enumeration</span>
</li>
<li class="flex items-start">
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
<span>Polynomial convergence through symbolic gradient descent</span>
</li>
<li class="flex items-start">
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
<span>Entropy minimization drives system to stable states</span>
</li>
<li class="flex items-start">
<i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i>
<span>No local minima for satisfiable instances</span>
</li>
</ul>
</div>
</div>
</div>
</main>
<script>
// Initialize Feather Icons
feather.replace();
// DOM Elements
const hilbertCanvas = document.getElementById('hilbertCanvas');
const entropyChart = document.getElementById('entropyChart').getContext('2d');
const currentStateEl = document.getElementById('currentState');
const entropyValueEl = document.getElementById('entropyValue');
const timeStepEl = document.getElementById('timeStep');
const startBtn = document.getElementById('startBtn');
const resetBtn = document.getElementById('resetBtn');
const varCount = document.getElementById('varCount');
const clauseCount = document.getElementById('clauseCount');
const decayConstant = document.getElementById('decayConstant');
const varCountValue = document.getElementById('varCountValue');
const clauseCountValue = document.getElementById('clauseCountValue');
const decayValue = document.getElementById('decayValue');
const algorithmSteps = document.querySelectorAll('.algorithm-step');
// Simulation state
let simulationRunning = false;
let currentTime = 0;
let entropyData = [];
let currentState = '|Ψ₀⟩';
let primeStates = [];
let animationTimeline = null;
// Update parameter displays
varCount.addEventListener('input', () => {
varCountValue.textContent = varCount.value;
});
clauseCount.addEventListener('input', () => {
clauseCountValue.textContent = clauseCount.value;
});
decayConstant.addEventListener('input', () => {
decayValue.textContent = decayConstant.value;
});
// Initialize visualization
function initVisualization() {
hilbertCanvas.innerHTML = '';
primeStates = [];
// Create prime-number eigenstates
const primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29];
const n = parseInt(varCount.value);
for (let i = 0; i < n; i++) {
const prime = primes[i];
const state = document.createElement('div');
state.className = 'prime-state absolute w-16 h-16 rounded-full flex items-center justify-center text-white font-bold border-2 border-indigo-400';
state.style.left = `${20 + (i % 3) * 30}%`;
state.style.top = `${20 + Math.floor(i / 3) * 30}%`;
state.style.backgroundColor = `rgba(${50 + i * 20}, ${60 + i * 15}, ${200 + i * 5}, 0.7)`;
state.textContent = `|${prime}⟩`;
state.dataset.prime = prime;
state.dataset.index = i;
hilbertCanvas.appendChild(state);
primeStates.push(state);
}
// Reset state displays
currentStateEl.textContent = '|Ψ₀⟩';
entropyValueEl.textContent = 'S₀';
timeStepEl.textContent = 't = 0';
entropyData = [{time: 0, entropy: 100}];
drawEntropyChart();
}
// Draw entropy convergence chart
function drawEntropyChart() {
entropyChart.clearRect(0, 0, entropyChart.canvas.width, entropyChart.canvas.height);
if (entropyData.length === 0) return;
// Draw grid
entropyChart.strokeStyle = '#334155';
entropyChart.lineWidth = 1;
// Vertical grid lines
for (let i = 0; i <= 10; i++) {
const x = (i / 10) * entropyChart.canvas.width;
entropyChart.beginPath();
entropyChart.moveTo(x, 0);
entropyChart.lineTo(x, entropyChart.canvas.height);
entropyChart.stroke();
}
// Horizontal grid lines
for (let i = 0; i <= 5; i++) {
const y = (i / 5) * entropyChart.canvas.height;
entropyChart.beginPath();
entropyChart.moveTo(0, y);
entropyChart.lineTo(entropyChart.canvas.width, y);
entropyChart.stroke();
}
// Draw entropy curve
entropyChart.strokeStyle = '#4ade80';
entropyChart.lineWidth = 3;
entropyChart.beginPath();
for (let i = 0; i < entropyData.length; i++) {
const x = (entropyData[i].time / 100) * entropyChart.canvas.width;
const y = entropyChart.canvas.height - (entropyData[i].entropy / 100) * entropyChart.canvas.height;
if (i === 0) {
entropyChart.moveTo(x, y);
} else {
entropyChart.lineTo(x, y);
}
}
entropyChart.stroke();
}
// Animate the simulation
function animateSimulation() {
if (!simulationRunning) return;
currentTime++;
timeStepEl.textContent = `t = ${currentTime}`;
// Update entropy
const newEntropy = Math.max(0, 100 - currentTime * 5);
entropyValueEl.textContent = `S(t) = ${newEntropy.toFixed(1)}`;
entropyData.push({time: currentTime, entropy: newEntropy});
drawEntropyChart();
// Animate prime states
primeStates.forEach((state, index) => {
// Simulate phase changes
const phase = (currentTime + index) % 4;
const phases = ['0', 'π/2', 'π', '3π/2'];
// Update visual state
anime({
targets: state,
scale: [1, 1.1, 1],
backgroundColor: [
state.style.backgroundColor,
`rgba(${100 + index * 15}, ${120 + index * 10}, ${220 + index * 5}, 0.9)`,
state.style.backgroundColor
],
duration: 1000,
easing: 'easeInOutQuad'
});
// Add active class temporarily
state.classList.add('active-state');
setTimeout(() => {
state.classList.remove('active-state');
}, 1000);
});
// Update current state
if (currentTime < 10) {
currentStateEl.textContent = '|Ψ(t)⟩';
} else if (currentTime < 20) {
currentStateEl.textContent = '|Ψ*⟩';
// Highlight final step
algorithmSteps.forEach(step => step.classList.remove('current-step'));
algorithmSteps[5].classList.add('current-step');
}
// Update algorithm steps
if (currentTime >= 5 && currentTime < 10) {
algorithmSteps.forEach(step => step.classList.remove('current-step'));
algorithmSteps[3].classList.add('current-step');
} else if (currentTime >= 10 && currentTime < 15) {
algorithmSteps.forEach(step => step.classList.remove('current-step'));
algorithmSteps[4].classList.add('current-step');
}
// Continue animation or stop
if (currentTime < 25) {
setTimeout(animateSimulation, 800);
} else {
simulationRunning = false;
startBtn.textContent = 'Restart Simulation';
}
}
// Event Listeners
startBtn.addEventListener('click', () => {
if (!simulationRunning) {
simulationRunning = true;
startBtn.textContent = 'Running...';
animateSimulation();
}
});
resetBtn.addEventListener('click', () => {
simulationRunning = false;
currentTime = 0;
startBtn.textContent = 'Start Simulation';
initVisualization();
// Reset algorithm steps
algorithmSteps.forEach(step => step.classList.remove('current-step'));
algorithmSteps[0].classList.add('current-step');
});
// Initialize on load
window.addEventListener('load', () => {
initVisualization();
// Animate introduction
anime({
targets: '.prime-state',
scale: [0, 1],
opacity: [0, 1],
delay: anime.stagger(200),
duration: 1000,
easing: 'easeOutElastic'
});
});
</script>
</body>
</html>
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