zaremba-transfer-operator-cuda

Zaremba Transfer Operator Spectral Gaps

Computes spectral gaps of the transfer operator for Zaremba generators {1,...,5} using implicit Kronecker product + power iteration.

Note: The kernels Python binding for this repo is a stub only. The underlying CUDA kernel uses cuBLAS, pthreads, and multi-GPU orchestration that has not yet been refactored into a single torch-callable function. For now, use the standalone compiled binary (see below). Full get_kernel() support is planned.

Standalone Usage

nvcc -O3 -arch=sm_120 -o transfer_operator transfer_operator/transfer_operator.cu -lcublas -lcusolver -lm -lpthread
./transfer_operator [N] [phase] [max_m] [min_m]
# N: Chebyshev polynomial order (default 40)
# phase: 1=Hausdorff only, 2=congruence gaps only, 3=both (default 3)
# max_m: maximum modulus (default 100)
# min_m: minimum modulus (default 2)

Results

All computation results are open:

• Website: bigcompute.science
• Datasets: huggingface.co/cahlen
• Source: github.com/cahlen/idontknow

Citation

@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 Not peer-reviewed.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.