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Applied 4-primitive framework to Erdős Conjecture on Arithmetic Progressions.
Conjecture: If Σ_{a∈A} 1/a diverges, then A contains arbitrarily long APs.
Test parameters:
- n_max values: [50, 100, 200]
- Density values: [0.3, 0.5, 0.7]
- 27 dense sets generated
Results:
- High reciprocal sum sets: 1
- Low reciprocal sum sets: 26
- Avg AP length (high reciprocal): 5.00
- Avg AP length (low reciprocal): 4.85
- Correlation holds: True
4-primitive analysis:
- Field primitive (ρ(x⃗)): density, reciprocal sum, conjecture condition
- Shear primitive (G = AᵀA): translation rigidity, periodicity score, density deformation
- Spectral primitive (C = UΛUᵀ): set structure eigen decomposition, spectral radius
- Packet primitive (Γᵢ): APs as packets, max AP length, AP density
Findings:
- Field primitive captures conjecture condition (reciprocal sum)
- Shear primitive measures structural regularity (translation)
- Spectral primitive reveals additive structure
- Packet primitive captures AP witnesses
- Correlation holds: high reciprocal sum → longer APs
Framework validated for additive combinatorics problems.
Pipeline complete: 4 Erdős problems tested with 4-primitive framework.
Results saved to: 4-Infrastructure/shim/test_erdos_ap_4primitive_results.json
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| bin | ||
| config | ||
| drivers | ||
| exploit-infra/CATEGORY/TSM | ||
| gpu | ||
| hardware | ||
| infra | ||
| nano-kernel | ||
| NoDupeLabs | ||
| packaging | ||
| servo-fetch | ||
| shim | ||
| shims | ||
| surface | ||
| 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