2 problems

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Gubeladze's conjecture on the integer Carathéodory rank of normal polytopes
Gubeladze's conjecture. The coefficient $2$ in front of $n$ in the bound for the integer Carathéodory rank of normal polytopes cannot be improved.
Conjectureopendiscrete-geometry integer-caratheodory-rank normal-polytopesarXiv posted 2 days ago
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Sebő's integral Carathéodory property conjecture
Sebő's conjecture. The ICP holds for every $n$ -dimensional cone $C$ .
Conjecturerefutedconvex-cones hilbert-bases integer-caratheodory-rankarXiv posted 2 days ago

Gubeladze's conjecture on the integer Carathéodory rank of normal polytopes