{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OOWKAI3LGSSHXSC6UM32ZTNPE2","short_pith_number":"pith:OOWKAI3L","canonical_record":{"source":{"id":"1801.08751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-26T10:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"ecae944e6e0f95d21642b65e612498961e5cbc7081697405f5bbc04d06d93e89","abstract_canon_sha256":"d0bd84a3346b179b233da5df59dae6da5103e84ff88acaa0ea887514880a097c"},"schema_version":"1.0"},"canonical_sha256":"73aca0236b34a47bc85ea337accdaf268243ad496cd3fa522f9ceedd5e0fe516","source":{"kind":"arxiv","id":"1801.08751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08751","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08751v1","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08751","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"OOWKAI3LGSSH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OOWKAI3LGSSHXSC6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OOWKAI3L","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OOWKAI3LGSSHXSC6UM32ZTNPE2","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-26T10:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"ecae944e6e0f95d21642b65e612498961e5cbc7081697405f5bbc04d06d93e89","abstract_canon_sha256":"d0bd84a3346b179b233da5df59dae6da5103e84ff88acaa0ea887514880a097c"},"schema_version":"1.0"},"canonical_sha256":"73aca0236b34a47bc85ea337accdaf268243ad496cd3fa522f9ceedd5e0fe516","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:03.121695Z","signature_b64":"qOvW7TCwXIEM/UBGiwB4YjEyRihmvq9kRxFwNQb7KSmk6sZFsCALqI7g5H+hbKQyxoelJo4IL+FdHITxdpGnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73aca0236b34a47bc85ea337accdaf268243ad496cd3fa522f9ceedd5e0fe516","last_reissued_at":"2026-05-18T00:25:03.121248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:03.121248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08751","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shVUAAx7EKSIowRuRYDGwzKA6tD9v09k7WNhl16eghMwJ3pS/e/7QyXY0vZYKJjMFJ8UXE9VCpk0hn/++w3MCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:09:37.840484Z"},"content_sha256":"db593e9f33d53b0034aed69faac374c5cb5d0dbe41ce915a4e9ca03000fbe8bf","schema_version":"1.0","event_id":"sha256:db593e9f33d53b0034aed69faac374c5cb5d0dbe41ce915a4e9ca03000fbe8bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OOWKAI3LGSSHXSC6UM32ZTNPE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distances of optimal solutions of mixed-integer programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Joseph Paat, Robert Weismantel, Stefan Weltge","submitted_at":"2018-01-26T10:51:51Z","abstract_excerpt":"A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables and a parameter $ \\Delta $, which quantifies sub-determinants of the underlying linear inequalities. We show that this distance can be bounded in terms of $ \\Delta $ and the number of integer variables rather than the total number of variables. To this end, we make use of a result by Olson (1969) in additive combinatorics and demonstrate how it implies feasib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08751","kind":"arxiv","version":1},"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":"2026-05-18T00:25:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maPpjIPEc9AyO6BQivBZ4dIoxBpYZwCwzMrcSshNixKHdH+CZALK4AQuAmMH+GSYNrx3Y1ji2uiU5iQ7VLurCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:09:37.841181Z"},"content_sha256":"f2149a14b87470896d138ff609b1e84b8ed1adac7f438de628872134f753338b","schema_version":"1.0","event_id":"sha256:f2149a14b87470896d138ff609b1e84b8ed1adac7f438de628872134f753338b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/bundle.json","state_url":"https://pith.science/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/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":"2026-05-26T11:09:37Z","links":{"resolver":"https://pith.science/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2","bundle":"https://pith.science/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/bundle.json","state":"https://pith.science/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOWKAI3LGSSHXSC6UM32ZTNPE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OOWKAI3LGSSHXSC6UM32ZTNPE2","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":"d0bd84a3346b179b233da5df59dae6da5103e84ff88acaa0ea887514880a097c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-26T10:51:51Z","title_canon_sha256":"ecae944e6e0f95d21642b65e612498961e5cbc7081697405f5bbc04d06d93e89"},"schema_version":"1.0","source":{"id":"1801.08751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08751","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08751v1","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08751","created_at":"2026-05-18T00:25:03Z"},{"alias_kind":"pith_short_12","alias_value":"OOWKAI3LGSSH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OOWKAI3LGSSHXSC6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OOWKAI3L","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:f2149a14b87470896d138ff609b1e84b8ed1adac7f438de628872134f753338b","target":"graph","created_at":"2026-05-18T00:25:03Z","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 classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables and a parameter $ \\Delta $, which quantifies sub-determinants of the underlying linear inequalities. We show that this distance can be bounded in terms of $ \\Delta $ and the number of integer variables rather than the total number of variables. To this end, we make use of a result by Olson (1969) in additive combinatorics and demonstrate how it implies feasib","authors_text":"Joseph Paat, Robert Weismantel, Stefan Weltge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-26T10:51:51Z","title":"Distances of optimal solutions of mixed-integer programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08751","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:db593e9f33d53b0034aed69faac374c5cb5d0dbe41ce915a4e9ca03000fbe8bf","target":"record","created_at":"2026-05-18T00:25:03Z","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":"d0bd84a3346b179b233da5df59dae6da5103e84ff88acaa0ea887514880a097c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-26T10:51:51Z","title_canon_sha256":"ecae944e6e0f95d21642b65e612498961e5cbc7081697405f5bbc04d06d93e89"},"schema_version":"1.0","source":{"id":"1801.08751","kind":"arxiv","version":1}},"canonical_sha256":"73aca0236b34a47bc85ea337accdaf268243ad496cd3fa522f9ceedd5e0fe516","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73aca0236b34a47bc85ea337accdaf268243ad496cd3fa522f9ceedd5e0fe516","first_computed_at":"2026-05-18T00:25:03.121248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:03.121248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qOvW7TCwXIEM/UBGiwB4YjEyRihmvq9kRxFwNQb7KSmk6sZFsCALqI7g5H+hbKQyxoelJo4IL+FdHITxdpGnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:03.121695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db593e9f33d53b0034aed69faac374c5cb5d0dbe41ce915a4e9ca03000fbe8bf","sha256:f2149a14b87470896d138ff609b1e84b8ed1adac7f438de628872134f753338b"],"state_sha256":"50b3f732000e59a6cf6f1c937389117ba520c0bc2209a77b394f782a18ae3436"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4sgFUD+pWRb1x3kunNQPSLQQVWgmQ4f+bds705jeMz4SXuHA+pemYcgfDiMnCtK0d8ptGHYOLIbGdWgeVi7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:09:37.845251Z","bundle_sha256":"62961a400a77cc899c6877dd26cd3482e70588e0ad8de7b08ebf4f6e4f356870"}}