{"paper":{"title":"Ornamentation lattices and intreeval hypergraphic lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Sack, Antoine Abram, F\\'elix G\\'elinas, Jose Bastidas, Vincent Pilaud","submitted_at":"2025-08-03T05:57:04Z","abstract_excerpt":"Given a directed graph $D$ with transitive closure $\\operatorname{tc}(D)$ and path hypergraph $\\mathbb{P}(D)$, we study the connections between the (acyclic) reorientation poset of $\\operatorname{tc}(D)$, the (acyclic) sourcing poset of $\\mathbb{P}(D)$, and the (acyclic) ornamentation poset of $D$. Geometrically, the acyclic reorientation poset of $\\operatorname{tc}(D)$ (resp. the acyclic sourcing poset of $\\mathbb{P}(D)$) is the transitive closure of the skeleton of the graphical zonotope of $\\operatorname{tc}(D)$ (resp. of the hypergraphic polytope of $\\mathbb{P}(D)$) oriented in a linear di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01606","kind":"arxiv","version":1},"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/2508.01606/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"}