Brandon Schneider
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d9038dbc41
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test: 4-primitive framework applied to Erdős Conjecture on APs
Applied 4-primitive framework to Erdős Conjecture on Arithmetic Progressions.
Conjecture: If Σ_{a∈A} 1/a diverges, then A contains arbitrarily long APs.
Test parameters:
- n_max values: [50, 100, 200]
- Density values: [0.3, 0.5, 0.7]
- 27 dense sets generated
Results:
- High reciprocal sum sets: 1
- Low reciprocal sum sets: 26
- Avg AP length (high reciprocal): 5.00
- Avg AP length (low reciprocal): 4.85
- Correlation holds: True
4-primitive analysis:
- Field primitive (ρ(x⃗)): density, reciprocal sum, conjecture condition
- Shear primitive (G = AᵀA): translation rigidity, periodicity score, density deformation
- Spectral primitive (C = UΛUᵀ): set structure eigen decomposition, spectral radius
- Packet primitive (Γᵢ): APs as packets, max AP length, AP density
Findings:
- Field primitive captures conjecture condition (reciprocal sum)
- Shear primitive measures structural regularity (translation)
- Spectral primitive reveals additive structure
- Packet primitive captures AP witnesses
- Correlation holds: high reciprocal sum → longer APs
Framework validated for additive combinatorics problems.
Pipeline complete: 4 Erdős problems tested with 4-primitive framework.
Results saved to: 4-Infrastructure/shim/test_erdos_ap_4primitive_results.json
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2026-05-08 14:50:02 -05:00 |
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