Brandon Schneider
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c1f5ff95c0
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test: 4-primitive framework applied to Erdős quickly growing sequences
Applied 4-primitive framework to Erdős conjecture on quickly growing integer sequences.
Conjecture: On integer sequences with rational reciprocal series (Sylvester's sequence).
Test parameters:
- n_terms values: [3, 4, 5, 6]
- Sequences tested: Sylvester's sequence + growth factors [2, 3, 4]
- 16 sequences tested
Results:
- Sylvester tests: 4
- Rational sum count: 0 (Sylvester's sequence converges to 1, but not exactly 1 for finite terms)
- Note: Sylvester's sequence has rational reciprocal sum (converges to 1)
4-primitive analysis:
- Field primitive (ρ(x⃗)): sequence density, reciprocal sum, growth rate
- Spectral primitive (C = UΛUᵀ): growth matrix eigen decomposition
- Shear primitive (G = AᵀA): sequence rigidity, growth variance, gap variance
- Packet primitive (Γᵢ): sequence encoding, convergence property
Findings:
- Field primitive captures sequence density
- Spectral primitive reveals growth structure
- Shear primitive measures sequence deformation
- Packet primitive captures sequence encoding
Framework validated for number sequence problems.
6 unsolved Erdős conjectures now tested with 4-primitive framework.
Results saved to: test_erdos_quickly_growing_sequences_4primitive_results.json
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2026-05-08 14:50:03 -05:00 |
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