{"paper":{"title":"The poset of rational cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Joseph Gubeladze, Mateusz Micha{\\l}ek","submitted_at":"2016-06-07T10:21:02Z","abstract_excerpt":"We introduce a natural partial order on the set Cones(d) of rational cones in R^d. The poset NPol(d-1) of normal polytopes in R^{d-1} embeds into Cones(d) via the homogenization map. The order in Cones(d) is conjecturally the inclusion order. We prove this for d=3 and show a stronger version of the connectivity of Cones(d) for all d. Topological aspects of the conjecture are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02083","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}