cahlen/hausdorff-dimension-spectrum

---
license: cc-by-4.0
task_categories:
- tabular-classification
tags:
- mathematics
- continued-fractions
- fractal-geometry
- hausdorff-dimension
- spectral-theory
- gpu-computation
size_categories:
- 1M<n<10M
---

# Hausdorff Dimension Spectrum: All Subsets of {1,...,20}

First complete computation of the Hausdorff dimension of E_A for all 2^20 - 1 = 1,048,575 non-empty subsets A of {1,...,20}. Computed via transfer operator + Chebyshev collocation (N=40) on NVIDIA RTX 5090.

This dataset does not exist anywhere in the published literature.

## Files

- `spectrum_n5.csv` — All 31 subsets of {1,...,5}
- `spectrum_n10.csv` — All 1,023 subsets of {1,...,10}
- `spectrum_n20.csv` — All 1,048,575 subsets of {1,...,20} (main dataset, 61 MB)
- `metadata_*.json` — Computation parameters for each run
- `run_n20.log` / `run_n20_recompute.log` — Computation logs

## CSV Schema

| Column | Description |
|--------|-------------|
| `subset_mask` | Bitmask encoding the subset |
| `subset_digits` | Human-readable digit set, e.g. `{1,2,3}` |
| `cardinality` | Number of digits in subset |
| `max_digit_in_subset` | Largest digit |
| `dimension` | Hausdorff dimension dim_H(E_A), 15 significant digits |

## Key Values

| Subset | dim_H(E_A) |
|--------|-----------|
| {1,2} | 0.5313 |
| {1,2,3,4,5} | 0.8368 (Zaremba semigroup) |
| {1,...,10} | 0.9540 |
| {1,...,20} | 0.9653 |

## Method

Transfer operator with Chebyshev collocation at N=40 nodes. Hausdorff dimension computed as the unique s where the leading eigenvalue equals 1. Bisection with 55 steps for ~15 digit precision. Power iteration with 300 iterations per eigenvalue.

## Hardware

NVIDIA RTX 5090 (32 GB). Full n=20 computation: 4,343 seconds.

## Citation

```bibtex
@dataset{humphreys2026hausdorff,
author = {Humphreys, Cahlen},
title = {Hausdorff Dimension Spectrum for Continued Fraction Cantor Sets},
year = {2026},
publisher = {Hugging Face},
url = {https://huggingface.co/datasets/cahlen/hausdorff-dimension-spectrum}
}
```

## Source

- **Code**: [hausdorff-spectrum](https://github.com/cahlen/idontknow/tree/main/scripts/experiments/hausdorff-spectrum)
- **Findings**: [Digit 1 Dominance](https://bigcompute.science/findings/hausdorff-digit-one-dominance/)
- **Project**: [bigcompute.science](https://bigcompute.science)
- **MCP Server**: `mcp.bigcompute.science` (22 tools, no auth)
- **AGENTS.md**: [Contribution guide](https://github.com/cahlen/idontknow/blob/main/AGENTS.md)

## Citation

```bibtex
@misc{humphreys2026hausdorff_dimension_spectrum,
author = {Humphreys, Cahlen and Claude (Anthropic)},
title = {Hausdorff Dimension Spectrum for Continued Fraction Cantor Sets},
year = {2026},
publisher = {Hugging Face},
url = {https://huggingface.co/datasets/cahlen/hausdorff-dimension-spectrum}
}
```

Human-AI collaborative work (Cahlen Humphreys + Claude). Not independently peer-reviewed. All code and data open for verification. CC BY 4.0.