@article{operatorspectroscopyoftrainedlatticesamp,
  title = {Operator Spectroscopy of Trained Lattice Samplers},
  author = {Moxian Qian},
  year = {2026},
  eprint = {2605.11199},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.11199},
}