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We prove that the split rank of a rational pure-integer polyhedron is polynomially bounded in its input length, resolving a conjecture of Basu, Conforti, Di Summa, and Jiang. If the defining system has dense binary encoding length L, then O((L+1)⁹) split rounds suffice to reach the integer hull in arbitrary dimension.
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Bhardwaj et al. (2026) studied this question.
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