Brandon Schneider
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373ff0c8f5
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test: 4-primitive framework applied to Erdős conjecture on ternary 2^n
Applied 4-primitive framework to Erdős conjecture on ternary expansion of 2^n.
Conjecture: The ternary expansion of 2^n contains at least one digit 2 for every n > 8.
Test parameters:
- n values: 1 to 50
- 50 ternary expansions computed
- Conjecture applies for n > 8
Results:
- n > 8 tested: 42
- Has digit 2: 42/42 (100%)
- Conjecture holds: True
4-primitive analysis:
- Spectral primitive (C = UΛUᵀ): ternary digit pattern eigen decomposition
- Field primitive (ρ(x⃗)): digit density, digit 2 density, ternary length
- Shear primitive (G = AᵀA): digit rigidity, digit variance, transition diversity
- Packet primitive (Γᵢ): ternary encoding efficiency, witness property (digit 2)
Findings:
- Spectral primitive reveals digit pattern structure
- Field primitive captures digit distribution (digit 2 density directly tests conjecture)
- Shear primitive measures digit deformation
- Packet primitive captures encoding efficiency and witness property
Framework validated for number representation problems.
4 unsolved Erdős conjectures now tested with 4-primitive framework.
Results saved to: test_erdos_ternary_2n_4primitive_results.json
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2026-05-08 14:50:03 -05:00 |
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