{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6KJJ2SAKBN62EJMJ7SJL2B6DLA","short_pith_number":"pith:6KJJ2SAK","canonical_record":{"source":{"id":"1803.03455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-09T10:23:38Z","cross_cats_sorted":[],"title_canon_sha256":"37faea85118873e0100fd2c90550a07e832b4096b4c34e15be1324300de40d0f","abstract_canon_sha256":"530d07f4eae2709e0d393cdea2dd27844ce43dce8edb8f14b040e673e5b46434"},"schema_version":"1.0"},"canonical_sha256":"f2929d480a0b7da22589fc92bd07c35800a33a4acc44e25f9997421b849a70bc","source":{"kind":"arxiv","id":"1803.03455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03455","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03455v1","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03455","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"6KJJ2SAKBN62","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KJJ2SAKBN62EJMJ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KJJ2SAK","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6KJJ2SAKBN62EJMJ7SJL2B6DLA","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-09T10:23:38Z","cross_cats_sorted":[],"title_canon_sha256":"37faea85118873e0100fd2c90550a07e832b4096b4c34e15be1324300de40d0f","abstract_canon_sha256":"530d07f4eae2709e0d393cdea2dd27844ce43dce8edb8f14b040e673e5b46434"},"schema_version":"1.0"},"canonical_sha256":"f2929d480a0b7da22589fc92bd07c35800a33a4acc44e25f9997421b849a70bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:28.291833Z","signature_b64":"aczoiSWRGxmuklX6MerNHrfvH+5kXzXnnAlDqrSNwEWPIlEQpZVIn9OtJvhUSAFp+Pq98BJFeGeh2ky3V+KQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2929d480a0b7da22589fc92bd07c35800a33a4acc44e25f9997421b849a70bc","last_reissued_at":"2026-05-17T23:54:28.291305Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:28.291305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03455","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":"2026-05-17T23:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VvZ5jc1WL+X5g6Pop2V+Cmi/MIoM57YziqYdnUeHgp2DB/QaGqmFZ7/uwHglKBz50BGGlzqoQPRD43PCKKkZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:27:36.508259Z"},"content_sha256":"5d152dfc943e53365ea8d51d05a09d651cfe492148b6ad394094bee1192ba0c1","schema_version":"1.0","event_id":"sha256:5d152dfc943e53365ea8d51d05a09d651cfe492148b6ad394094bee1192ba0c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6KJJ2SAKBN62EJMJ7SJL2B6DLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel E. Steffy, Matthias Miltenberger, Ted Ralphs","submitted_at":"2018-03-09T10:23:38Z","abstract_excerpt":"We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03455","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":"2026-05-17T23:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tqXu5qxM1x52Q7dpw3PgFrGbS6WcDLozap7rsm7Q0H3vaQYFm5fjYfCyx7quDKU9BOpXO1+lTidlEKOdIbQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:27:36.508947Z"},"content_sha256":"cca1b231dc45a62a7187399fdee7371f0ef2ab13b26c91b4af495967dedd02b4","schema_version":"1.0","event_id":"sha256:cca1b231dc45a62a7187399fdee7371f0ef2ab13b26c91b4af495967dedd02b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/bundle.json","state_url":"https://pith.science/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/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":"2026-05-26T09:27:36Z","links":{"resolver":"https://pith.science/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA","bundle":"https://pith.science/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/bundle.json","state":"https://pith.science/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KJJ2SAKBN62EJMJ7SJL2B6DLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6KJJ2SAKBN62EJMJ7SJL2B6DLA","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":"530d07f4eae2709e0d393cdea2dd27844ce43dce8edb8f14b040e673e5b46434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-09T10:23:38Z","title_canon_sha256":"37faea85118873e0100fd2c90550a07e832b4096b4c34e15be1324300de40d0f"},"schema_version":"1.0","source":{"id":"1803.03455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03455","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03455v1","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03455","created_at":"2026-05-17T23:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"6KJJ2SAKBN62","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KJJ2SAKBN62EJMJ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KJJ2SAK","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:cca1b231dc45a62a7187399fdee7371f0ef2ab13b26c91b4af495967dedd02b4","target":"graph","created_at":"2026-05-17T23:54:28Z","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":"We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this be","authors_text":"Daniel E. Steffy, Matthias Miltenberger, Ted Ralphs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-09T10:23:38Z","title":"Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03455","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":"sha256:5d152dfc943e53365ea8d51d05a09d651cfe492148b6ad394094bee1192ba0c1","target":"record","created_at":"2026-05-17T23:54:28Z","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":"530d07f4eae2709e0d393cdea2dd27844ce43dce8edb8f14b040e673e5b46434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-09T10:23:38Z","title_canon_sha256":"37faea85118873e0100fd2c90550a07e832b4096b4c34e15be1324300de40d0f"},"schema_version":"1.0","source":{"id":"1803.03455","kind":"arxiv","version":1}},"canonical_sha256":"f2929d480a0b7da22589fc92bd07c35800a33a4acc44e25f9997421b849a70bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2929d480a0b7da22589fc92bd07c35800a33a4acc44e25f9997421b849a70bc","first_computed_at":"2026-05-17T23:54:28.291305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:28.291305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aczoiSWRGxmuklX6MerNHrfvH+5kXzXnnAlDqrSNwEWPIlEQpZVIn9OtJvhUSAFp+Pq98BJFeGeh2ky3V+KQCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:28.291833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d152dfc943e53365ea8d51d05a09d651cfe492148b6ad394094bee1192ba0c1","sha256:cca1b231dc45a62a7187399fdee7371f0ef2ab13b26c91b4af495967dedd02b4"],"state_sha256":"13fa9013eb4158a758d75f7b4784b6d9eec0bd639875876432b1b536144cc596"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iMGmoRLwe8Ai9KU0sVOl1qygCYm9OGBdL8J6qmHb7rI1ULJFqQR6omv9Z2vTrnrJ5OKCCQvWemAZF8N7C4mmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:27:36.512606Z","bundle_sha256":"cf02f92ea302ebd101374f885760e220dfd8ffb9f078a2e9ed359e5b139201a1"}}