# LogicBench-1K — Dataset Statistics (camera-ready)

**Version:** 1.0.1  
**Generated:** 2026-06-08T19:05:59Z  
**Samples:** 1,000 (700/100/200 train/val/test)

## Sample diversity

| Metric | Value |
|--------|------:|
| Unique gate mixtures | 343 |
| Mixture coverage (unique / samples) | 34.3% |
| Gates per diagram (mean ± std) | 6.174 ± 3.699 |
| Gates per diagram (median [Q1, Q3]) | 5.0 [4.0, 7.0] |
| Gates per diagram (range) | 1–31 |
| Diagrams with no edges | 19 |

### Node-count histogram

| Bin (gates) | Count |
|-------------|------:|
| 1-5 | 576 |
| 6-10 | 343 |
| 11-15 | 49 |
| 16-20 | 18 |
| 21-31 | 14 |

## Topology distribution

### Gate-type frequencies (global)

| Gate | Count | Share |
|------|------:|------:|
| AND | 1,492 | 24.2% |
| NAND | 915 | 14.8% |
| NOR | 597 | 9.7% |
| NOT | 1,389 | 22.5% |
| OR | 894 | 14.5% |
| XNOR | 258 | 4.2% |
| XOR | 629 | 10.2% |

### Edge-count summary

| Statistic | Value |
|-----------|------:|
| Total directed edges | 6,423 |
| Edges per diagram (mean ± std) | 6.423 ± 5.636 |
| Edges per diagram (median) | 5.0 |
| Edges per diagram (range) | 0–57 |
| Mean directed density | 0.2355 |

### Edge-count histogram

| Bin (edges) | Count |
|-------------|------:|
| 0 | 19 |
| 1-5 | 544 |
| 6-10 | 298 |
| 11-20 | 114 |
| 21-57 | 25 |

### Split-stratified summary

| Split | *n* | Unique mixtures | Gates (mean) | Edges (mean) | Density |
|-------|----:|----------------:|-------------:|-------------:|--------:|
| Train | 700 | 261 | 5.91 | 6.08 | 0.2399 |
| Val | 100 | 73 | 6.77 | 7.04 | 0.2148 |
| Test | 200 | 128 | 6.8 | 7.315 | 0.2305 |

## Paper-ready summary

The corpus comprises 1,000 annotated diagrams with 6,174 gates and 6,423 directed edges. Sample diversity spans 343 unique gate mixtures (34.3% coverage). Diagrams contain 1–31 gates (mean 6.174, median 5.0) and 0–57 edges (mean 6.423, median 5.0). Gate-type and topology statistics are stratified by the official 700/100/200 train/validation/test split in `metadata/statistics.json`.

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*Auto-generated by `scripts/generate_statistics.py`. Machine-readable source: [`statistics.json`](statistics.json).*