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  "problem_id": "vibemathed:two-counterexamples-geometry-of-numbers",
  "title": "Two Counterexamples in the Geometry of Numbers",
  "canonical_statement": "The paper gives counterexamples in dimensions eight and nine to two problems: the Cartesian-product problem posed by Cassels for critical determinants and formulated by Zong for lattice packings, and a question raised by Sarnak, formulated as a conjecture by Chiu, on whether height among unit-volume flat tori is minimized by a lattice maximizing its shortest nonzero vector.",
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      "title": "arXiv",
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