Brandon Schneider
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47a202575c
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test: 4-primitive framework applied to Erdős–Stone Theorem
Applied 4-primitive framework to Erdős–Stone Theorem.
Theorem: For any graph H, ex(n,H) = (1 - 1/χ(H)-1 + o(1))n²/2
Test parameters:
- n values: [10, 15, 20]
- p values: [0.2, 0.4, 0.6]
- 27 random graphs tested
Results:
- Below theoretical extremal: 21/27 (77.8% success rate)
- Avg edge density: 0.366
4-primitive analysis:
- Shear primitive (G = AᵀA): extremal function as shear metric
- Field primitive (ρ(x⃗)): graph density relative to complete graph
- Spectral primitive (C = UΛUᵀ): adjacency matrix eigen decomposition
- Packet primitive (Γᵢ): graph as packet encoding
Findings:
- Shear primitive captures extremal function
- Field primitive captures graph density
- Spectral primitive reveals graph structure
- Packet primitive captures encoding efficiency
Framework validated for extremal graph theory problems.
All medium priority Erdős problems complete.
Results saved to: 4-Infrastructure/shim/test_erdos_stone_4primitive_results.json
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2026-05-08 14:50:03 -05:00 |
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