{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7NRBNSSWML7KFCSBNPVXFP2IPV","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":"4549c26af4acb287d647b9d98f662ef0b3b2cb8e6377a7a7f2f99469ca83df80","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-11-15T22:07:58Z","title_canon_sha256":"e970d90b3ec5243a94a0af33c6f9ebb8de56429a9406780d313a99f0e9f2f4ed"},"schema_version":"1.0","source":{"id":"1911.06894","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.06894","created_at":"2026-07-05T01:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1911.06894v3","created_at":"2026-07-05T01:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.06894","created_at":"2026-07-05T01:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"7NRBNSSWML7K","created_at":"2026-07-05T01:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"7NRBNSSWML7KFCSB","created_at":"2026-07-05T01:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"7NRBNSSW","created_at":"2026-07-05T01:02:57Z"}],"graph_snapshots":[{"event_id":"sha256:f4abc328d4561676ab4f2ff4b78fe2510742870a36a68b1dc4380f29fe5e199e","target":"graph","created_at":"2026-07-05T01:02:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.06894/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018) and Buchheim, Crama and Rodr\\'iguez-Heck (European Journal of Operations Research, 2019). We also present an algorithm that finds these extra monomials for a given polynomial to yield an integral relaxation polytope or determines that no such set o","authors_text":"Christopher Hojny, Marc E. Pfetsch, Matthias Walter","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-11-15T22:07:58Z","title":"Integrality of Linearizations of Polynomials over Binary Variables using Additional Monomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.06894","kind":"arxiv","version":3},"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":"sha256:78e81e106c52b520156d0e39e79e3730a6d77be771d0a687491dabf9950cdb08","target":"record","created_at":"2026-07-05T01:02:57Z","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":"4549c26af4acb287d647b9d98f662ef0b3b2cb8e6377a7a7f2f99469ca83df80","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-11-15T22:07:58Z","title_canon_sha256":"e970d90b3ec5243a94a0af33c6f9ebb8de56429a9406780d313a99f0e9f2f4ed"},"schema_version":"1.0","source":{"id":"1911.06894","kind":"arxiv","version":3}},"canonical_sha256":"fb6216ca5662fea28a416beb72bf487d68a79a6080a67b2b7b33f665e318cbb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb6216ca5662fea28a416beb72bf487d68a79a6080a67b2b7b33f665e318cbb9","first_computed_at":"2026-07-05T01:02:57.298349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:02:57.298349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"71cXf8e6t89cj6/nAr4/cLXWj85h79BhpVSoqPfrkb2KQQce4fO5w/9AKTpHpv8FyZcZPR7wEBg0s1yW/9FjDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:02:57.298754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.06894","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78e81e106c52b520156d0e39e79e3730a6d77be771d0a687491dabf9950cdb08","sha256:f4abc328d4561676ab4f2ff4b78fe2510742870a36a68b1dc4380f29fe5e199e"],"state_sha256":"e4b9ad7b1712d77f306e0ae3d9072241c61ca147f6ed8c78986a5103f9fab442"}