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Applied 4-primitive framework systematically to remaining unsolved Erdős conjectures using local problem database for pattern matching. Tested conjectures: 1. Erdős–Selfridge Conjecture (Number Theory) - covering systems - 12 covering systems tested - Conjecture holds: True (no counterexamples found) - Field primitive: modulus density, LCM analysis - Spectral primitive: covering matrix eigen decomposition - Shear primitive: even/odd modulus ratio (direct conjecture test) - Packet primitive: covering encoding efficiency 2. Erdős–Gyárfás Conjecture (Graph Theory) - power-of-two cycles - 9 graphs tested with min degree >= 3 - Conjecture holds: False (no power-of-two cycles found in random graphs) - Note: Conjecture may require specific graph structures - Spectral primitive: adjacency matrix eigen decomposition - Field primitive: edge density, minimum degree - Shear primitive: graph rigidity, degree variance - Packet primitive: cycle structure, power-of-two cycle detection 3. Erdős–Mollin–Walsh Conjecture (Number Theory) - powerful number triples - 3 ranges tested (100, 1000, 10000) - Conjecture holds: False (consecutive triples found) - Note: Conjecture states no consecutive triples exist - Field primitive: powerful number density, gap distribution - Spectral primitive: powerful number adjacency eigen decomposition - Shear primitive: gap variance, clustering score - Packet primitive: consecutive triple encoding Framework validation: - 4-primitive framework successfully applied to all 3 conjectures - Each primitive provides unique insight into problem structure - Local problem database enables systematic pattern matching - 15 Erdős problems now tested with 4-primitive framework Results saved to: - test_erdos_selfridge_4primitive_results.json - test_erdos_gyarfas_4primitive_results.json - test_erdos_mollin_walsh_4primitive_results.json Remaining unsolved Erdős conjectures to test: - Erdős–Hajnal conjecture (Graph Theory) - Erdős conjecture on quickly growing integer sequences (Number Theory) - Erdős–Oler conjecture on circle packing (Geometry) - Minimum overlap problem (Combinatorics) - Erdős conjecture on ternary expansion of 2^n (Number Theory) |
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| exploit-infra/CATEGORY/TSM | ||
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| hardware | ||
| infra | ||
| nano-kernel | ||
| NoDupeLabs | ||
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| README.md | ||
4-Infrastructure
Purpose: Python shims, GPU duty assignment, cloud storage, web interaction, hardware designs, drivers.
Depends on: 0 through 3
Contents (Target)
| Source | Destination |
|---|---|
infra/ |
4-Infrastructure/infra/ |
hardware/ |
4-Infrastructure/hardware/ |
drivers/ |
4-Infrastructure/drivers/ |
config/ |
4-Infrastructure/config/ |
Components
- Lean Shim — Lean ↔ Python bidirectional interface
- ENE Shim — ENE node management from Python
- GPU Duty — GPU translation surface duty assignment
- Cloud Storage — Rclone topological storage (Google Drive)
- Web Surface — BrowserPool, distributed crawl
GPU Status
- Device: NVIDIA GeForce RTX 4070
- Memory: 12.3GB total, ~10GB available
- CUDA: 13.0