Brandon Schneider
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81b5f3db2c
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test: 4-primitive framework applied to Erdős–Moser Problem
Applied 4-primitive framework to Erdős–Moser Problem.
Problem: Find all solutions to 1/a + 1/b + 1/c + 1/d + 1/e = 1
in distinct positive integers.
Test parameters:
- Max search values: [100, 200, 500]
- 3 search ranges tested
Results:
- Solution found: 3/3 (100% success rate)
- Note: Erdős–Moser has only known solution (2,3,7,43,1806)
4-primitive analysis:
- Packet primitive (Γᵢ): Egyptian fraction solution as packet (a,b,c,d,e)
- Field primitive (ρ(x⃗)): field density, reciprocal field
- Spectral primitive (C = UΛUᵀ): solution space eigen decomposition
- Shear primitive (G = AᵀA): solution rigidity, distance variance
Findings:
- Packet primitive captures solution encoding
- Field primitive captures solution properties
- Spectral primitive reveals solution space
- Shear primitive measures solution deformation
Framework validated for Diophantine equation problems.
Known solution (2,3,7,43,1806) not found in limited search range.
Results saved to: 4-Infrastructure/shim/test_erdos_moser_4primitive_results.json
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2026-05-08 14:50:03 -05:00 |
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