Two Counterexamples in the Geometry of Numbers
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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Occurred: Jul 13, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Two Counterexamples in the Geometry of Numbers · Geometry of numbers
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
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VibeMathed
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Nihar Gargava
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ChatGPT 5 + Codex
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This event attributed to Nihar Gargava
This event attributed to ChatGPT 5 + Codex