@article{thepropagationfieldageometricsubstrateth,
  title = {The Propagation Field: A Geometric Substrate Theory of Deep Learning},
  author = {Xingrui Gu},
  year = {2026},
  eprint = {2605.08529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.08529},
}