@article{thespectralgeometryofthoughtphasetransit,
  title = {The Spectral Geometry of Thought: Phase Transitions, Instruction Reversal, Token-Level Dynamics, and Perfect Correctness Prediction in How Transformers Reason},
  author = {Yi Liu},
  year = {2026},
  eprint = {2604.15350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2604.15350},
}