experiment stringclasses 1
value | date timestamp[s]date 2026-03-29 00:00:00 2026-03-29 00:00:00 | hardware stringclasses 1
value | max_digit int64 5 20 | num_subsets int64 31 1.05M | chebyshev_order int64 40 40 | bisection_steps int64 55 55 | power_iterations int64 300 300 | precision_digits int64 15 15 | total_runtime_seconds float64 1.8 8.65k | novel bool 1
class | description stringclasses 4
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
hausdorff-dimension-spectrum | 2026-03-29T00:00:00 | RTX 5090 32GB | 10 | 1,023 | 40 | 55 | 300 | 15 | 3.8 | true | First complete Hausdorff dimension spectrum for all subsets of {1,...,10} |
hausdorff-dimension-spectrum | 2026-03-29T00:00:00 | RTX 5090 32GB | 15 | 32,767 | 40 | 55 | 300 | 15 | 126.1 | true | First complete Hausdorff dimension spectrum for all subsets of {1,...,15} |
hausdorff-dimension-spectrum | 2026-03-29T00:00:00 | RTX 5090 32GB | 20 | 1,048,575 | 40 | 55 | 300 | 15 | 8,654.9 | true | First complete Hausdorff dimension spectrum for all subsets of {1,...,20} |
hausdorff-dimension-spectrum | 2026-03-29T00:00:00 | RTX 5090 32GB | 5 | 31 | 40 | 55 | 300 | 15 | 1.8 | true | First complete Hausdorff dimension spectrum for all subsets of {1,...,5} |
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 runrun_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
@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
- Findings: Digit 1 Dominance
- Project: bigcompute.science
- MCP Server:
mcp.bigcompute.science(22 tools, no auth) - AGENTS.md: Contribution guide
Citation
@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.
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