{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NSZ6ITZUYYO2AHGSRFSQWNKYIR","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":"5254464c4c21011c0ade03e147fb4966ba24b0fbbb861198866d822648761ff5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2023-10-11T03:34:17Z","title_canon_sha256":"847bd41067d4fc49bd78ee8a8d9cd19ada9ed461b0b464c26b3a6c5595059355"},"schema_version":"1.0","source":{"id":"2310.07168","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.07168","created_at":"2026-07-05T08:32:09Z"},{"alias_kind":"arxiv_version","alias_value":"2310.07168v3","created_at":"2026-07-05T08:32:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.07168","created_at":"2026-07-05T08:32:09Z"},{"alias_kind":"pith_short_12","alias_value":"NSZ6ITZUYYO2","created_at":"2026-07-05T08:32:09Z"},{"alias_kind":"pith_short_16","alias_value":"NSZ6ITZUYYO2AHGS","created_at":"2026-07-05T08:32:09Z"},{"alias_kind":"pith_short_8","alias_value":"NSZ6ITZU","created_at":"2026-07-05T08:32:09Z"}],"graph_snapshots":[{"event_id":"sha256:aac168320ccbb7bf4d0dfede4a49d4cb51d6c1840eafa36b504efa587018977b","target":"graph","created_at":"2026-07-05T08:32:09Z","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/2310.07168/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming (MIP) relaxations. Our relaxations rely on ideal formulations of convex hulls of outer-functions over a combinatorial structure that captures local inner-function structure. The resulting relaxations often require fewer variables and are tighter than currently prevalent ones. Finally, we provide computational evidence to demonstrate that our relaxations close approximately 60-","authors_text":"Mohit Tawarmalani, Taotao He","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2023-10-11T03:34:17Z","title":"MIP Relaxations in Factorable Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.07168","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":"sha256:5046add0832518a3e8478a569f41baa0591e9650b01b33d3f34f8428d447cc11","target":"record","created_at":"2026-07-05T08:32:09Z","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":"5254464c4c21011c0ade03e147fb4966ba24b0fbbb861198866d822648761ff5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2023-10-11T03:34:17Z","title_canon_sha256":"847bd41067d4fc49bd78ee8a8d9cd19ada9ed461b0b464c26b3a6c5595059355"},"schema_version":"1.0","source":{"id":"2310.07168","kind":"arxiv","version":3}},"canonical_sha256":"6cb3e44f34c61da01cd289650b35584444978e20c3f6bc3f0eaf762ad4a77065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb3e44f34c61da01cd289650b35584444978e20c3f6bc3f0eaf762ad4a77065","first_computed_at":"2026-07-05T08:32:09.400114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:32:09.400114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iy1hQ/MDPh6+Ux6lbxGVG7cuzP5JRxnEpx14ESD4W0+Iv9LyPhrcZBhNY+N9lgXHYm+RcSJ3+iLsrzOz49nDCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:32:09.400692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.07168","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5046add0832518a3e8478a569f41baa0591e9650b01b33d3f34f8428d447cc11","sha256:aac168320ccbb7bf4d0dfede4a49d4cb51d6c1840eafa36b504efa587018977b"],"state_sha256":"94986fd551968766caa26694f834080068a566a477ec4ebc118fef22bf83e1bb"}