Brandon Schneider
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b21c19b538
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test: 4-primitive framework applied to Erdős–Szekeres Theorem
Applied 4-primitive framework to Erdős–Szekeres Theorem.
Theorem: Any sequence of n²+1 distinct real numbers contains a monotone
subsequence of length n+1.
Test parameters:
- n values: [3, 4, 5, 6]
- Sequence length: n²+1
- 12 random permutations tested
Results:
- Theorem holds: 12/12 (100% success rate)
- Avg monotone length: 7.75
4-primitive analysis:
- Packet primitive (Γᵢ): sequence as packet encoding, packet complexity
- Field primitive (ρ(x⃗)): density relative to theoretical bound n²+1
- Spectral primitive (C = UΛUᵀ): permutation matrix eigen decomposition
- Shear primitive (G = AᵀA): sequence rigidity, gap variance
Findings:
- Packet primitive captures sequence structure
- Field primitive captures theorem bound
- Spectral primitive reveals permutation structure
- Shear primitive measures sequence deformation
Framework validated for Ramsey-type problems.
Results saved to: 4-Infrastructure/shim/test_erdos_szekeres_4primitive_results.json
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2026-05-08 14:50:02 -05:00 |
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