{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:Z5XWJDHI4Z6LPSE4MUP63VSFVD","short_pith_number":"pith:Z5XWJDHI","canonical_record":{"source":{"id":"2311.03885","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T10:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"cbb570da6393ce3e5a144a56185f87452c793ce7e3b0419090f5f1683c863cbc","abstract_canon_sha256":"9379224c4f9e9cd0d56af4a025058e80df171df0edc78b1b02b90ef015522c29"},"schema_version":"1.0"},"canonical_sha256":"cf6f648ce8e67cb7c89c651fedd645a8fd79f3d81e6b4132c30174d3e10bb766","source":{"kind":"arxiv","id":"2311.03885","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03885","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03885v3","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03885","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_12","alias_value":"Z5XWJDHI4Z6L","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_16","alias_value":"Z5XWJDHI4Z6LPSE4","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_8","alias_value":"Z5XWJDHI","created_at":"2026-07-05T10:59:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:Z5XWJDHI4Z6LPSE4MUP63VSFVD","target":"record","payload":{"canonical_record":{"source":{"id":"2311.03885","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T10:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"cbb570da6393ce3e5a144a56185f87452c793ce7e3b0419090f5f1683c863cbc","abstract_canon_sha256":"9379224c4f9e9cd0d56af4a025058e80df171df0edc78b1b02b90ef015522c29"},"schema_version":"1.0"},"canonical_sha256":"cf6f648ce8e67cb7c89c651fedd645a8fd79f3d81e6b4132c30174d3e10bb766","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:22.709149Z","signature_b64":"skAf2z0ztRKTbrosKHdQ9yiyar95Yukt6bKR0L4DrudsRYN0Ro8LGW3sQaISZ77ab1RuA/7kQjU/vbrqSLsfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf6f648ce8e67cb7c89c651fedd645a8fd79f3d81e6b4132c30174d3e10bb766","last_reissued_at":"2026-07-05T10:59:22.708654Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:22.708654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.03885","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:59:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wSApaf4hHy4t2owcBId57BbFD7fnEkYdlAcRId7ZHxkof777E93TmpxFjP/MgOlCrjh+iWRXdtxJj65psNTAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:14:33.217276Z"},"content_sha256":"2a6697e2cbbae245728b7777e7fed88cc994fff8db5bc40c44dc0d6cc888710d","schema_version":"1.0","event_id":"sha256:2a6697e2cbbae245728b7777e7fed88cc994fff8db5bc40c44dc0d6cc888710d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:Z5XWJDHI4Z6LPSE4MUP63VSFVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Branching Rules for Optimizing Range and Order-Based Objective Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrea Lodi, Bart van Rossum, Rui Chen","submitted_at":"2023-11-07T10:59:25Z","abstract_excerpt":"We consider range minimization problems featuring exponentially many variables, as frequently arising in fairness-oriented or bi-objective optimization. While branch and price is successful at solving cost-oriented problems with many variables, the performance of classical branch-and-price algorithms for range minimization is drastically impaired by weak linear programming relaxations. We propose range branching, a generic branching rule that directly tackles this issue and can be used on top of problem-specific branching schemes. We show several desirable properties of range branching and sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03885","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.03885/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:59:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ur3roJMO5m/FeeJ5KYLapb22Ioj/mm97IHlrDRpbualOjJkZqbEDvv4le0gzSu8Cp4P4P3QgwOxhOu7E6zOxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:14:33.218503Z"},"content_sha256":"6a5baad44de5bd75dda04969f3bd3173869b71dfd6875eec00af42ffd0819084","schema_version":"1.0","event_id":"sha256:6a5baad44de5bd75dda04969f3bd3173869b71dfd6875eec00af42ffd0819084"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/bundle.json","state_url":"https://pith.science/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/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":"2026-08-23T16:14:33Z","links":{"resolver":"https://pith.science/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD","bundle":"https://pith.science/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/bundle.json","state":"https://pith.science/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5XWJDHI4Z6LPSE4MUP63VSFVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Z5XWJDHI4Z6LPSE4MUP63VSFVD","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":"9379224c4f9e9cd0d56af4a025058e80df171df0edc78b1b02b90ef015522c29","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T10:59:25Z","title_canon_sha256":"cbb570da6393ce3e5a144a56185f87452c793ce7e3b0419090f5f1683c863cbc"},"schema_version":"1.0","source":{"id":"2311.03885","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03885","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03885v3","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03885","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_12","alias_value":"Z5XWJDHI4Z6L","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_16","alias_value":"Z5XWJDHI4Z6LPSE4","created_at":"2026-07-05T10:59:22Z"},{"alias_kind":"pith_short_8","alias_value":"Z5XWJDHI","created_at":"2026-07-05T10:59:22Z"}],"graph_snapshots":[{"event_id":"sha256:6a5baad44de5bd75dda04969f3bd3173869b71dfd6875eec00af42ffd0819084","target":"graph","created_at":"2026-07-05T10:59:22Z","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/2311.03885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider range minimization problems featuring exponentially many variables, as frequently arising in fairness-oriented or bi-objective optimization. While branch and price is successful at solving cost-oriented problems with many variables, the performance of classical branch-and-price algorithms for range minimization is drastically impaired by weak linear programming relaxations. We propose range branching, a generic branching rule that directly tackles this issue and can be used on top of problem-specific branching schemes. We show several desirable properties of range branching and sho","authors_text":"Andrea Lodi, Bart van Rossum, Rui Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T10:59:25Z","title":"Efficient Branching Rules for Optimizing Range and Order-Based Objective Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03885","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":"sha256:2a6697e2cbbae245728b7777e7fed88cc994fff8db5bc40c44dc0d6cc888710d","target":"record","created_at":"2026-07-05T10:59:22Z","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":"9379224c4f9e9cd0d56af4a025058e80df171df0edc78b1b02b90ef015522c29","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T10:59:25Z","title_canon_sha256":"cbb570da6393ce3e5a144a56185f87452c793ce7e3b0419090f5f1683c863cbc"},"schema_version":"1.0","source":{"id":"2311.03885","kind":"arxiv","version":3}},"canonical_sha256":"cf6f648ce8e67cb7c89c651fedd645a8fd79f3d81e6b4132c30174d3e10bb766","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6f648ce8e67cb7c89c651fedd645a8fd79f3d81e6b4132c30174d3e10bb766","first_computed_at":"2026-07-05T10:59:22.708654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:22.708654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skAf2z0ztRKTbrosKHdQ9yiyar95Yukt6bKR0L4DrudsRYN0Ro8LGW3sQaISZ77ab1RuA/7kQjU/vbrqSLsfAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:22.709149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.03885","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a6697e2cbbae245728b7777e7fed88cc994fff8db5bc40c44dc0d6cc888710d","sha256:6a5baad44de5bd75dda04969f3bd3173869b71dfd6875eec00af42ffd0819084"],"state_sha256":"69797c0baa744ee71dd82833e6ca90656fa76bc362357bd6055c8821c133a082"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FKnGIrOwF5PxpmBLPxbAg8kI9uhDbSVYdKP72xJoVZtNroSMUUI8OqPdLajRi+47QA5Tti0T5iJBM9l9vRiQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T16:14:33.227625Z","bundle_sha256":"5ca698c2ec32989c932899d33ebcbcc6829aa20e8e4cdce64f52e5072f3119fb"}}