{"paper":{"title":"Preserving Hodge Vectors of Lattice Polytopes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Benjamin Nill, Vadym Kurylenko","submitted_at":"2026-02-24T10:45:18Z","abstract_excerpt":"Given lattice polytopes $P_1, \\ldots, P_k$ contained in a $k$-dimensional subspace $U \\subseteq \\mathbb{R}^d$ and a $d$-dimensional lattice polytope $Q \\subset \\mathbb{R}^d$, we compute the Hodge vector of the Cayley polytope $P_1 * \\cdots * P_k * Q$, and show that it equals the mixed volume of $P_1, \\ldots, P_k$ times the Hodge vector of the projection of $Q$ along $U$. Here, the Hodge vector of a lattice polytope is its local $h^*$-vector with leading and trailing zeroes removed. This result allows finding infinitely many high-dimensional lattice polytopes with the same Hodge vector that are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.20765","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.20765/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}