{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NTIEFTKL26XIPYG5XVO5D5W5FE","short_pith_number":"pith:NTIEFTKL","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"},"canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","source":{"kind":"arxiv","id":"1611.08832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08832","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08832v2","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08832","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"NTIEFTKL26XI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NTIEFTKL26XIPYG5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NTIEFTKL","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NTIEFTKL26XIPYG5XVO5D5W5FE","target":"record","payload":{"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"},"canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","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"},"source_kind":"arxiv","source_id":"1611.08832","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxzgmIMIrmaHuStWc0VU5dUydCMqaQ6tBVRi6rs6tTigjLXmZ3WBN4DBSPo8OmL/v8v7IULUWpfAxSY8LVSbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:47.671362Z"},"content_sha256":"37bd5eadfce740fd477681ab732bd99ab8b236badcacbb84a4a208152586d4f8","schema_version":"1.0","event_id":"sha256:37bd5eadfce740fd477681ab732bd99ab8b236badcacbb84a4a208152586d4f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NTIEFTKL26XIPYG5XVO5D5W5FE","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1Nwl19NXgGoZmxlJUCnxzxnsT49GE8aj1TThsgg8x2p8QG1JIesnyJNHULVVA94olk/GdVUbpdXVNRCBbMQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:40:47.672028Z"},"content_sha256":"e223519ea5267faec2493581df13d2813950b7710ca30b7222df3062bd3ba0d5","schema_version":"1.0","event_id":"sha256:e223519ea5267faec2493581df13d2813950b7710ca30b7222df3062bd3ba0d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/bundle.json","state_url":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T03:40:47Z","links":{"resolver":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE","bundle":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/bundle.json","state":"https://pith.science/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTIEFTKL26XIPYG5XVO5D5W5FE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NTIEFTKL26XIPYG5XVO5D5W5FE","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":"0820a29c02d18ad97134d8751ae2909d405a102fcafbb73652505c225f26cd6e","cross_cats_sorted":["cs.DM","cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-27T12:27:03Z","title_canon_sha256":"caefef234d4feddfe32ad43dc7360bbb76b9ce8053fcd2ed08d3b89b7ab3ea95"},"schema_version":"1.0","source":{"id":"1611.08832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08832","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08832v2","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08832","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"NTIEFTKL26XI","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NTIEFTKL26XIPYG5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NTIEFTKL","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:e223519ea5267faec2493581df13d2813950b7710ca30b7222df3062bd3ba0d5","target":"graph","created_at":"2026-05-17T23:57:07Z","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":"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","authors_text":"Ambros Gleixner, Daniel E. Steffy, Kevin K. H. Cheung","cross_cats":["cs.DM","cs.MS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-27T12:27:03Z","title":"Verifying Integer Programming Results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08832","kind":"arxiv","version":2},"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":"sha256:37bd5eadfce740fd477681ab732bd99ab8b236badcacbb84a4a208152586d4f8","target":"record","created_at":"2026-05-17T23:57:07Z","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":"0820a29c02d18ad97134d8751ae2909d405a102fcafbb73652505c225f26cd6e","cross_cats_sorted":["cs.DM","cs.MS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-27T12:27:03Z","title_canon_sha256":"caefef234d4feddfe32ad43dc7360bbb76b9ce8053fcd2ed08d3b89b7ab3ea95"},"schema_version":"1.0","source":{"id":"1611.08832","kind":"arxiv","version":2}},"canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cd042cd4bd7ae87e0ddbd5dd1f6dd29140d25dfda4bab816eb16ff87ddb9292","first_computed_at":"2026-05-17T23:57:07.907146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:07.907146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xyb4iipmiBFMn9MzmfZzHgeY7pGVGipb38DuQGBMruklJdNuATJCR0yxIXvcnNEOI2pSHT4jc3V05JQKBlotAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:07.907516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37bd5eadfce740fd477681ab732bd99ab8b236badcacbb84a4a208152586d4f8","sha256:e223519ea5267faec2493581df13d2813950b7710ca30b7222df3062bd3ba0d5"],"state_sha256":"b6d3870ff986525a81133b37109c55dbb45d6caace89feb2490da94a165aaac4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7z/Ok02GGKPBuA7yGeOTAU6jSVxUIZkPbBIDfWCJ+c+U3P9KOb9IWrrGR40u/OTWTaUauoLP1DQCj3eCV4WRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:40:47.675718Z","bundle_sha256":"eeb7ad435447f4e4e59061630396ad330958fe6dffebcedd1456aae3bd9f8c31"}}