{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WTWZI26Q5RKWYA6AF2NPYTIBUQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bbdf332911cc673c3dbb41286144606ce75084880d93ed169308f15d25a31625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T19:06:33Z","title_canon_sha256":"29789dbb14149dd2f2547fce71bb782185a30076ab4ae501aa8cd154fd7a1550"},"schema_version":"1.0","source":{"id":"1711.00891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00891","created_at":"2026-05-18T00:31:24Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00891v1","created_at":"2026-05-18T00:31:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00891","created_at":"2026-05-18T00:31:24Z"},{"alias_kind":"pith_short_12","alias_value":"WTWZI26Q5RKW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WTWZI26Q5RKWYA6A","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WTWZI26Q","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:270ec42c917698a26caf60757385652d81b59a3d090fcbd1fdeed23ef40f6bbb","target":"graph","created_at":"2026-05-18T00:31:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A celebrated theorem of Balas gives a linear mixed-integer formulation for the union of two nonempty polytopes whose relaxation gives the convex hull of this union. The number of inequalities in Balas formulation is linear in the number of inequalities that describe the two polytopes and the number of variables is doubled. In this paper we show that this is best possible: in every dimension there exist two nonempty polytopes such that if a formulation for the convex hull of their union has a number of inequalities that is polynomial in the number of inequalities that describe the two polytopes","authors_text":"Marco Di Summa, Michele Conforti, Yuri Faenza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T19:06:33Z","title":"Balas formulation for the union of polytopes is optimal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00891","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dfe3311bb92b59bf284d0241f4799a96e8a37d6ed12ebff6815b67659d55044c","target":"record","created_at":"2026-05-18T00:31:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bbdf332911cc673c3dbb41286144606ce75084880d93ed169308f15d25a31625","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-02T19:06:33Z","title_canon_sha256":"29789dbb14149dd2f2547fce71bb782185a30076ab4ae501aa8cd154fd7a1550"},"schema_version":"1.0","source":{"id":"1711.00891","kind":"arxiv","version":1}},"canonical_sha256":"b4ed946bd0ec556c03c02e9afc4d01a403295d6c546553492d803e39f018a434","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4ed946bd0ec556c03c02e9afc4d01a403295d6c546553492d803e39f018a434","first_computed_at":"2026-05-18T00:31:24.578445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:24.578445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9f6wsieEoJGtPfonkAXPNK2cYTQLwJ5GGtV3fDN5qBCyk8taUeIM2zVXePtjN3UHAuJ2Dv/lOUMXIRup5kjJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:24.578947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfe3311bb92b59bf284d0241f4799a96e8a37d6ed12ebff6815b67659d55044c","sha256:270ec42c917698a26caf60757385652d81b59a3d090fcbd1fdeed23ef40f6bbb"],"state_sha256":"e23e8e30cda9036d317c258dac7b9c5350c4ad4f5e937760d544ccf4fb415d33"}