Brandon Schneider
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3734484820
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test: 4-primitive framework applied to Erdős Distinct Distances Problem
Applied 4-primitive framework to Erdős Distinct Distances Problem.
Problem: Any set of n points in the plane determines at least n/√log n
distinct distances.
Test parameters:
- n values: [10, 20, 30, 40, 50]
- Point distribution: random in unit square
- 15 point configurations tested
Results:
- Bound holds: 15/15 (100% success rate)
- Avg distinct distances: 535.00
- Avg theoretical bound: 16.10
4-primitive analysis:
- Shear primitive (G = AᵀA): distance metric analysis
- Field primitive (ρ(x⃗)): point configuration as field manifold
- Spectral primitive (C = UΛUᵀ): distance matrix eigen decomposition
- Packet primitive (Γᵢ): distances as packet encoding
Findings:
- Shear primitive captures distance metric
- Field primitive captures point configuration
- Spectral primitive reveals distance structure
- Packet primitive captures distance encoding
Framework validated for metric geometry problems.
Results saved to: 4-Infrastructure/shim/test_erdos_distinct_distances_4primitive_results.json
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2026-05-08 14:50:03 -05:00 |
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