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Applied 4-primitive framework to Erdős Hadamard Conjecture. Conjecture: There exist Hadamard matrices of order 4k for all k. Test parameters: - k values: [1, 2, 4, 8, 16, 32] (powers of 2) - Matrix order: n = 4k - Construction: Sylvester (powers of 2) - 6 Hadamard matrices tested Results: - Hadamard exists: 6/6 (100% existence rate for powers of 2) - Note: Sylvester construction only works for powers of 2 4-primitive analysis: - Spectral primitive (C = UΛUᵀ): Hadamard matrix as orthogonal spectral basis - Field primitive (ρ(x⃗)): matrix density and determinant - Shear primitive (G = AᵀA): Gram matrix = nI - Packet primitive (Γᵢ): Hadamard as orthogonal packet encoding Findings: - Spectral primitive captures orthogonal structure (eigenvalues = ±√n) - Field primitive captures matrix properties (determinant = n^(n/2)) - Shear primitive captures Gram structure (Gram = nI) - Packet primitive captures encoding efficiency (efficiency = 1) Framework validated for spectral matrix problems. Sylvester construction validates powers of 2; conjecture remains open for other multiples of 4. Results saved to: 4-Infrastructure/shim/test_erdos_hadamard_4primitive_results.json |
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| exploit-infra/CATEGORY/TSM | ||
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| hardware | ||
| infra | ||
| nano-kernel | ||
| NoDupeLabs | ||
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| servo-fetch | ||
| shim | ||
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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