{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NTIEFTKL26XIPYG5XVO5D5W5FE","short_pith_number":"pith:NTIEFTKL","schema_version":"1.0","canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","source":{"kind":"arxiv","id":"1611.08832","version":2},"attestation_state":"computed","paper":{"title":"Verifying Integer Programming Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.MS"],"primary_cat":"math.OC","authors_text":"Ambros Gleixner, Daniel E. Steffy, Kevin K. H. Cheung","submitted_at":"2016-11-27T12:27:03Z","abstract_excerpt":"Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certi"},"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":"1611.08832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-27T12:27:03Z","cross_cats_sorted":["cs.DM","cs.MS"],"title_canon_sha256":"caefef234d4feddfe32ad43dc7360bbb76b9ce8053fcd2ed08d3b89b7ab3ea95","abstract_canon_sha256":"0820a29c02d18ad97134d8751ae2909d405a102fcafbb73652505c225f26cd6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:07.907516Z","signature_b64":"Xyb4iipmiBFMn9MzmfZzHgeY7pGVGipb38DuQGBMruklJdNuATJCR0yxIXvcnNEOI2pSHT4jc3V05JQKBlotAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","last_reissued_at":"2026-05-17T23:57:07.907146Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:07.907146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Verifying Integer Programming Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.MS"],"primary_cat":"math.OC","authors_text":"Ambros Gleixner, Daniel E. Steffy, Kevin K. H. Cheung","submitted_at":"2016-11-27T12:27:03Z","abstract_excerpt":"Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MILP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format, illustrating its capabilities and structure through examples. The certi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08832","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":"1611.08832","created_at":"2026-05-17T23:57:07.907205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08832v2","created_at":"2026-05-17T23:57:07.907205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08832","created_at":"2026-05-17T23:57:07.907205+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTIEFTKL26XI","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTIEFTKL26XIPYG5","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTIEFTKL","created_at":"2026-05-18T12:30:36.002864+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/NTIEFTKL26XIPYG5XVO5D5W5FE","json":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE.json","graph_json":"https://pith.science/api/pith-number/NTIEFTKL26XIPYG5XVO5D5W5FE/graph.json","events_json":"https://pith.science/api/pith-number/NTIEFTKL26XIPYG5XVO5D5W5FE/events.json","paper":"https://pith.science/paper/NTIEFTKL"},"agent_actions":{"view_html":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE","download_json":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE.json","view_paper":"https://pith.science/paper/NTIEFTKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08832&json=true","fetch_graph":"https://pith.science/api/pith-number/NTIEFTKL26XIPYG5XVO5D5W5FE/graph.json","fetch_events":"https://pith.science/api/pith-number/NTIEFTKL26XIPYG5XVO5D5W5FE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/action/storage_attestation","attest_author":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/action/author_attestation","sign_citation":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/action/citation_signature","submit_replication":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/action/replication_record"}},"created_at":"2026-05-17T23:57:07.907205+00:00","updated_at":"2026-05-17T23:57:07.907205+00:00"}