---
license: mit
tags:
  - kernels
  - cuda
  - minkowski-question-mark
  - singularity-spectrum
  - thermodynamic-formalism
  - number-theory
datasets:
  - cahlen/continued-fraction-spectra
---

# Minkowski Question-Mark Singularity Spectrum

Computes the singularity spectrum f(alpha) of the Minkowski ?(x) function via thermodynamic formalism.

## Usage

```python
import torch
from kernels import get_kernel

kernel = get_kernel("cahlen/minkowski-spectrum-cuda")
result = minkowski.compute_tau(q_values, max_digit=50, chebyshev_order=40)
```

## Compile (standalone)

```bash
nvcc -O3 -arch=sm_90 -o minkowski_spectrum minkowski_spectrum/minkowski_spectrum.cu -lm
```

## Results

All computation results are open:
- **Website**: [bigcompute.science](https://bigcompute.science)
- **Datasets**: [huggingface.co/cahlen](https://huggingface.co/cahlen)
- **Source**: [github.com/cahlen/idontknow](https://github.com/cahlen/idontknow)

## Citation

```bibtex
@misc{humphreys2026bigcompute,
  author = {Humphreys, Cahlen},
  title = {bigcompute.science: GPU-Accelerated Computational Mathematics},
  year = {2026},
  url = {https://bigcompute.science}
}
```

*Human-AI collaborative. Not peer-reviewed. All code and data open.*