{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UAG5QFRQHBAVXNALSOJUEB7MPJ","short_pith_number":"pith:UAG5QFRQ","schema_version":"1.0","canonical_sha256":"a00dd8163038415bb40b93934207ec7a681b84584e0a9538504488c3e4938d63","source":{"kind":"arxiv","id":"1412.2520","version":2},"attestation_state":"computed","paper":{"title":"Note on the Complexity of the Mixed-Integer Hull of a Polyhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Robert Hildebrand, Robert Weismantel, Timm Oertel","submitted_at":"2014-12-08T11:29:23Z","abstract_excerpt":"We study the complexity of computing the mixed-integer hull $\\operatorname{conv}(P\\cap\\mathbb{Z}^n\\times\\mathbb{R}^d)$ of a polyhedron $P$. Given an inequality description, with one integer variable, the mixed-integer hull can have exponentially many vertices and facets in $d$. For $n,d$ fixed, we give an algorithm to find the mixed integer hull in polynomial time. Given $P=\\operatorname{conv}(V)$ and $n$ fixed, we compute a vertex description of the mixed-integer hull in polynomial time and give bounds on the number of vertices of the mixed integer hull."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.2520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-08T11:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"40e62add7929a7a0720b283da061b1755ed74ec8cf55cbd0871ee5164fbd437f","abstract_canon_sha256":"7d2bbefeceee3beccf5a2576683cb2b72fea31162dd5efc4dc95553905ebd8de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:18.366917Z","signature_b64":"BZkQVgh9e2xij/5rY37aI/z3i53nIa5sZIy8+scM3z8dI0orgJ/jgDuGsfWEe4MXzhVD/r2IvJMqV7mygJqYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a00dd8163038415bb40b93934207ec7a681b84584e0a9538504488c3e4938d63","last_reissued_at":"2026-05-18T02:25:18.366563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:18.366563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on the Complexity of the Mixed-Integer Hull of a Polyhedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Robert Hildebrand, Robert Weismantel, Timm Oertel","submitted_at":"2014-12-08T11:29:23Z","abstract_excerpt":"We study the complexity of computing the mixed-integer hull $\\operatorname{conv}(P\\cap\\mathbb{Z}^n\\times\\mathbb{R}^d)$ of a polyhedron $P$. Given an inequality description, with one integer variable, the mixed-integer hull can have exponentially many vertices and facets in $d$. For $n,d$ fixed, we give an algorithm to find the mixed integer hull in polynomial time. Given $P=\\operatorname{conv}(V)$ and $n$ fixed, we compute a vertex description of the mixed-integer hull in polynomial time and give bounds on the number of vertices of the mixed integer hull."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2520","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.2520","created_at":"2026-05-18T02:25:18.366626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2520v2","created_at":"2026-05-18T02:25:18.366626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2520","created_at":"2026-05-18T02:25:18.366626+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAG5QFRQHBAV","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAG5QFRQHBAVXNAL","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAG5QFRQ","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ","json":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ.json","graph_json":"https://pith.science/api/pith-number/UAG5QFRQHBAVXNALSOJUEB7MPJ/graph.json","events_json":"https://pith.science/api/pith-number/UAG5QFRQHBAVXNALSOJUEB7MPJ/events.json","paper":"https://pith.science/paper/UAG5QFRQ"},"agent_actions":{"view_html":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ","download_json":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ.json","view_paper":"https://pith.science/paper/UAG5QFRQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2520&json=true","fetch_graph":"https://pith.science/api/pith-number/UAG5QFRQHBAVXNALSOJUEB7MPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/UAG5QFRQHBAVXNALSOJUEB7MPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ/action/storage_attestation","attest_author":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ/action/author_attestation","sign_citation":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ/action/citation_signature","submit_replication":"https://pith.science/pith/UAG5QFRQHBAVXNALSOJUEB7MPJ/action/replication_record"}},"created_at":"2026-05-18T02:25:18.366626+00:00","updated_at":"2026-05-18T02:25:18.366626+00:00"}