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<h1 class="text-4xl font-medium text-gray-900 mb-4">Technical Documentation</h1>
<p class="text-xl text-gray-600 max-w-3xl">Complete reference for the Geometric Flow Cathedral optimization pipeline, including API specifications, configuration guides, and implementation details.</p>
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<span class="w-8 h-8 rounded-lg bg-primary-100 text-primary-600 flex items-center justify-center text-sm">01</span>
Overview
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<p>The Geometric Flow Cathedral implements a novel approach to traffic optimization by integrating geometric constraints into machine learning pipelines. The system leverages:</p>
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<li><strong>√14 Ratchet Decay:</strong> A decay factor derived from the square root of 14, applied to prevent overfitting and ensure smooth convergence.</li>
<li><strong>24-Fold Geometric Filtering:</strong> Temporal filtering based on prime spoke hours (1, 5, 7, 11, 13, 17, 19, 23) to capture cyclical traffic patterns.</li>
<li><strong>19.1° Phase Correction:</strong> Standing wave phase offset at 46.875Hz for sensor data synchronization.</li>
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Installation
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<div class="bg-gray-800 px-4 py-2 text-xs text-gray-400 font-mono border-b border-gray-700">bash</div>
<pre class="p-4 text-sm text-gray-300 overflow-x-auto"><code># Clone the repository
git clone https://github.com/google/geometric-flow-cathedral.git
cd geometric-flow-cathedral
# Install dependencies
pip install -r requirements.txt
# Configure environment variables
cp .env.example .env
# Initialize the pipeline
python -m gfc init</code></pre>
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<span class="w-8 h-8 rounded-lg bg-primary-100 text-primary-600 flex items-center justify-center text-sm">03</span>
Configuration
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<th class="p-4 border-b border-gray-200 font-medium text-gray-900">Parameter</th>
<th class="p-4 border-b border-gray-200 font-medium text-gray-900">Type</th>
<th class="p-4 border-b border-gray-200 font-medium text-gray-900">Default</th>
<th class="p-4 border-b border-gray-200 font-medium text-gray-900">Description</th>
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<td class="p-4 font-mono text-sm text-primary-600">RATchet_DECAY</td>
<td class="p-4 text-sm">float</td>
<td class="p-4 font-mono text-sm">0.267</td>
<td class="p-4 text-sm">1 - 1/√14 decay factor</td>
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<td class="p-4 font-mono text-sm text-primary-600">PHASE_OFFSET</td>
<td class="p-4 text-sm">float</td>
<td class="p-4 font-mono text-sm">19.1</td>
<td class="p-4 text-sm">Phase correction in degrees</td>
</tr>
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<td class="p-4 font-mono text-sm text-primary-600">PRIME_SPOKES</td>
<td class="p-4 text-sm">list</td>
<td class="p-4 font-mono text-sm">[1,5,7,11,13,17,19,23]</td>
<td class="p-4 text-sm">Active temporal filtering hours</td>
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<td class="p-4 font-mono text-sm text-primary-600">CONSTRAINT_BLEND</td>
<td class="p-4 text-sm">float</td>
<td class="p-4 font-mono text-sm">0.5</td>
<td class="p-4 text-sm">Geometric constraint weight (0-1)</td>
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API Reference
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<h3 class="font-mono text-lg text-gray-900">POST /api/v1/optimize</h3>
<span class="px-3 py-1 bg-green-100 text-green-700 rounded-full text-xs font-medium">Stable</span>
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<p class="text-gray-600 mb-4">Submit traffic data for real-time geometric optimization.</p>
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<pre class="p-4 text-sm text-gray-300 overflow-x-auto"><code>{
"sensor_data": {
"flow_rate": 120.5,
"timestamp": "2024-01-15T14:30:00Z",
"location_id": "intersection_42"
},
"constraints": {
"apply_ratchet": true,
"phase_correction": 19.1
}
}</code></pre>
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Examples
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<h3 class="font-medium text-gray-900">Urban Traffic Flow</h3>
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<p class="text-sm text-gray-600">Optimize signal timing across a 24-block grid using geometric constraints.</p>
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<h3 class="font-medium text-gray-900">Freeway Merge Optimization</h3>
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<p class="text-sm text-gray-600">Reduce congestion at highway on-ramps using predictive modeling.</p>
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