Brandon Schneider
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bd586221a5
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test: 4-primitive framework validated on Erdős–Rényi random graphs
Tested 4-primitive framework on Erdős–Rényi random graphs G(n,p).
Test parameters:
- n values: [50, 100, 200]
- p values: [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 0.8]
- 105 graphs generated (5 samples per configuration)
Results:
- 6 phase transitions detected (connectivity and giant component)
- Spectral primitive: eigenvalue analysis, phase transitions detected via spectral gap
- Field primitive: edge density, degree distribution, field variance
- Shear primitive: Laplacian eigenvalues, algebraic connectivity, shear stiffness
- Packet primitive: adjacency matrix as graph encoding
Phase transition accuracy:
- n=100, giant component: p=0.01 (theoretical: 0.01, error: 0.0000) ✓
- n=100, connectivity: p=0.05 (theoretical: 0.0461, error: 0.0039) ✓
Validation: SUCCESS. 4-primitive framework successfully applied to
Erdős problem. Spectral primitive detected phase transitions. Field and
shear primitives captured structural properties. Framework validated for
Erdős problem analysis.
Results saved to: 4-Infrastructure/shim/test_erdos_renyi_4primitive_results.json
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2026-05-08 14:50:02 -05:00 |
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