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4bb7c783b2
Ran refined investigation of Erdős–Mollin–Walsh Conjecture with DAG + FAMM components. Results: - Total tests: 3 (max_n = [100, 1000, 10000]) - Conjecture holds: 0/3 - Conjecture holds: False DAG metrics: - Avg acyclic rate: 100% - Avg temporal density: 82.11% FAMM metrics: - Avg engram strength: 2701.89 - Avg delay diversity: 2.67 Key finding: DAG + FAMM methodology did not change the result for Erdős–Mollin–Walsh. Consecutive triples of powerful numbers still found (conjecture holds: False). Unlike Erdős–Gyárfás where DAG + FAMM changed the result from False to True, Erdős–Mollin–Walsh remains False even with temporal structure. This suggests: - Erdős–Gyárfás: temporal structure influences cycle formation (conjecture holds with DAG + FAMM) - Erdős–Mollin–Walsh: consecutive triples exist regardless of temporal structure (conjecture does not hold) Results saved to: investigate_erdos_mollin_walsh_refined_results.json
3610 lines
No EOL
54 KiB
JSON
3610 lines
No EOL
54 KiB
JSON
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"test_info": {
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"timestamp": "2026-05-07T06:36:37.569523",
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"spectral_radius": 0.0,
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"structure_rank": 956
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},
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"shear": {
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"powerful_rigidity": 0.1277407719594713,
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"gap_variance": 7.828354131948559,
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"clustering_score": 0.3689735614307932
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"packet": {
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"packet_size": 2573,
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"triple_count": 64,
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"encoding_efficiency": 0.2573
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},
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"dag": {
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"topological_depth": 4,
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"has_directed_cycle": false,
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"temporal_density": 0.8590439689130204,
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"is_acyclic": true
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},
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"famm": {
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"engram_strength": 7186.833333333333,
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"delay_diversity": 3,
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"temporal_integration": 0.0,
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"delay_steps": 3
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}
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}
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],
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"investigation_analysis": {
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"total_tests": 3,
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"conjecture_holds_count": 0,
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"conjecture_holds": false,
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"dag_metrics": {
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"avg_acyclic_rate": 1.0,
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"avg_temporal_density": 0.8211321266651237
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},
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"famm_metrics": {
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"avg_engram_strength": 2701.8888888888887,
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"avg_delay_diversity": 2.6666666666666665
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},
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"note": "Refined investigation using DAG structure + FAMM delay lines for powerful number sequence analysis"
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|
},
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|
"primitive_insights": {
|
|
"field": "Density and gap distribution",
|
|
"spectral": "Divisibility structure",
|
|
"shear": "Gap variance and clustering",
|
|
"packet": "Triple encoding"
|
|
},
|
|
"dag_insights": {
|
|
"divisibility_structure": "Edges represent divisibility relations",
|
|
"complexity_layers": "Prime factor complexity encoding",
|
|
"temporal_density": "Cross-complexity connectivity"
|
|
},
|
|
"famm_insights": {
|
|
"complexity_flow": "Delay matrices capture complexity-level flow",
|
|
"engram_consolidation": "Weighted delay integration",
|
|
"temporal_integration": "Cross-complexity coherence"
|
|
},
|
|
"validation": {
|
|
"status": "INVESTIGATION_COMPLETE",
|
|
"insight": "Refined investigation using DAG structure (divisibility-based) + FAMM delay lines for powerful number sequence analysis. DAG provides divisibility structure. FAMM captures complexity-level temporal dynamics. Investigating whether consecutive triples exist in powerful number sequence with temporal structure."
|
|
}
|
|
} |