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78 lines
2.6 KiB
Python
78 lines
2.6 KiB
Python
#!/usr/bin/env python3
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"""
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Hadwiger-Nelson Audit: The Chromatic Number of the Plane
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RGFlow on Unit Distance Graph Colorings.
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"""
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import sys
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import numpy as np
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from pathlib import Path
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import logging
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# Add parent directory to path
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sys.path.insert(0, str(Path(__file__).parent.parent.parent))
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sys.path.insert(0, str(Path(__file__).parent.parent.parent / "4-Infrastructure"))
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sys.path.insert(0, str(Path(__file__).parent.parent.parent / "0-Core-Formalism"))
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from scripts.rgflow_blind_detector import BlindDetector
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logging.basicConfig(level=logging.ERROR)
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def run_hadwiger_audit():
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print("--- HADWIGER-NELSON INFORMATIC AUDIT ---")
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# We simulate a "Patch" of the plane with a Unit Distance Graph
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# We check if a k-coloring is "Scale-Stable"
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def check_unit_violations(points, colors, k):
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# Points: (N, 2) coords
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# Colors: (N,) ints
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violations = 0
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for i in range(len(points)):
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for j in range(i + 1, len(points)):
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dist = np.linalg.norm(points[i] - points[j])
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if np.abs(dist - 1.0) < 0.05: # Unit distance tolerance
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if colors[i] == colors[j]:
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violations += 1
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return violations
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detector = BlindDetector()
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# Number of colors to test
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for k in [4, 5, 6, 7]:
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print(f"\nTesting k={k} colors...")
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# Simulate a set of 100 points in a high-density UD-graph
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num_points = 100
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points = np.random.uniform(0, 10, (num_points, 2))
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colors = np.random.randint(0, k, num_points)
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violations = check_unit_violations(points, colors, k)
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# Mapping Violations to Informatic State
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if violations > 0:
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# The coloring is sabotaged by the rule of the plane
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sigma_q = 1.0 - (violations / (num_points * 2))
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else:
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# The coloring is lawful (at least locally)
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sigma_q = 2.0
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state = detector.calculate_window_state('ACGT'*100) # Template
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state.sigma_q = float(sigma_q)
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(lawful_now, lawful_under_flow, _, _, _, _, _, depth, _, _) = \
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detector.adaptation_eq.evaluate_state(state)
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print(f" Unit Violations: {violations}")
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print(f" Informatic Sigma: {sigma_q:.4f}")
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print(f" Manifold Depth: {depth}/10")
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if lawful_under_flow and depth >= 10:
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print(f" [+] RESULT: LAWFUL COLORING AT k={k}")
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else:
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print(f" [!] RESULT: INFORMATIC COLLAPSE (k={k} is insufficient)")
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print("\n--- AUDIT COMPLETE ---")
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if __name__ == "__main__":
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run_hadwiger_audit()
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