@article{bubblenecessitytheorem,
  title = {Bubble Necessity Theorem},
  author = {Tomohiro Hirano and Alexis Akira Toda},
  year = {2023},
  eprint = {2305.08268},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2305.08268v5},
}