{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:CDW65GW7HRPTNLY7FYINHVH7V3","short_pith_number":"pith:CDW65GW7","canonical_record":{"source":{"id":"2312.14836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2023-12-22T17:09:34Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"503bd45ba11381d8e018e25859ccbb98a605966696b6a95695805f5db92edcca","abstract_canon_sha256":"89d945baf08000a074dfe30a407d938044e0cb785357745199f4096db5d8e47f"},"schema_version":"1.0"},"canonical_sha256":"10edee9adf3c5f36af1f2e10d3d4ffaee69e4381fd33c0cc89ef356a63a90305","source":{"kind":"arxiv","id":"2312.14836","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.14836","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"2312.14836v1","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.14836","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"CDW65GW7HRPT","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"CDW65GW7HRPTNLY7","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"CDW65GW7","created_at":"2026-07-05T07:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:CDW65GW7HRPTNLY7FYINHVH7V3","target":"record","payload":{"canonical_record":{"source":{"id":"2312.14836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2023-12-22T17:09:34Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"503bd45ba11381d8e018e25859ccbb98a605966696b6a95695805f5db92edcca","abstract_canon_sha256":"89d945baf08000a074dfe30a407d938044e0cb785357745199f4096db5d8e47f"},"schema_version":"1.0"},"canonical_sha256":"10edee9adf3c5f36af1f2e10d3d4ffaee69e4381fd33c0cc89ef356a63a90305","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:27:20.508045Z","signature_b64":"9fkzC8ejb702UHq7a8Lfwp6lXuD4OLKIAqq+2liA+Fg9JOzYKYbL6qOvMEVr2ojiIa+3Gi2cI27H0V+iQ7X/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10edee9adf3c5f36af1f2e10d3d4ffaee69e4381fd33c0cc89ef356a63a90305","last_reissued_at":"2026-07-05T07:27:20.507566Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:27:20.507566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.14836","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":"2026-07-05T07:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reDDMd9GZMQJ8IWK86DeMsmYHRJGUre+uYcd1NBiBWPiC0hd9oo7xxAeinl1nTs4k1CC0NICWfdHHJd3ZUcNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:52:43.936568Z"},"content_sha256":"1519c557ef90dc273ef781abc5f85b970acd1ca3f776a3596a0f30b0fc115d37","schema_version":"1.0","event_id":"sha256:1519c557ef90dc273ef781abc5f85b970acd1ca3f776a3596a0f30b0fc115d37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:CDW65GW7HRPTNLY7FYINHVH7V3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Lagrangian Multipliers for the Travelling Salesman Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"cs.AI","authors_text":"Aaron Ferber, Augustin Parjadis, Bistra Dilkina, Louis-Martin Rousseau, Quentin Cappart","submitted_at":"2023-12-22T17:09:34Z","abstract_excerpt":"Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.14836","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.14836/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":"2026-07-05T07:27:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKhMn0HQUghTaW09OzWPYWl3dhRbjzsonlwdHdZM07bp6+fl/1FjwFWe8VZ+ZtcRbD0tw5xelG9EQ6K/Q6PBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:52:43.937115Z"},"content_sha256":"e0b11430598786315aaaf264faa79aee25c160cf39f0cbd2f76b70fa1e00fac2","schema_version":"1.0","event_id":"sha256:e0b11430598786315aaaf264faa79aee25c160cf39f0cbd2f76b70fa1e00fac2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDW65GW7HRPTNLY7FYINHVH7V3/bundle.json","state_url":"https://pith.science/pith/CDW65GW7HRPTNLY7FYINHVH7V3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDW65GW7HRPTNLY7FYINHVH7V3/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":"2026-08-18T08:52:43Z","links":{"resolver":"https://pith.science/pith/CDW65GW7HRPTNLY7FYINHVH7V3","bundle":"https://pith.science/pith/CDW65GW7HRPTNLY7FYINHVH7V3/bundle.json","state":"https://pith.science/pith/CDW65GW7HRPTNLY7FYINHVH7V3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDW65GW7HRPTNLY7FYINHVH7V3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CDW65GW7HRPTNLY7FYINHVH7V3","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":"89d945baf08000a074dfe30a407d938044e0cb785357745199f4096db5d8e47f","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2023-12-22T17:09:34Z","title_canon_sha256":"503bd45ba11381d8e018e25859ccbb98a605966696b6a95695805f5db92edcca"},"schema_version":"1.0","source":{"id":"2312.14836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.14836","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"arxiv_version","alias_value":"2312.14836v1","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.14836","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_12","alias_value":"CDW65GW7HRPT","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"CDW65GW7HRPTNLY7","created_at":"2026-07-05T07:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"CDW65GW7","created_at":"2026-07-05T07:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e0b11430598786315aaaf264faa79aee25c160cf39f0cbd2f76b70fa1e00fac2","target":"graph","created_at":"2026-07-05T07:27:20Z","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/2312.14836/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning appro","authors_text":"Aaron Ferber, Augustin Parjadis, Bistra Dilkina, Louis-Martin Rousseau, Quentin Cappart","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2023-12-22T17:09:34Z","title":"Learning Lagrangian Multipliers for the Travelling Salesman Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.14836","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":"sha256:1519c557ef90dc273ef781abc5f85b970acd1ca3f776a3596a0f30b0fc115d37","target":"record","created_at":"2026-07-05T07:27:20Z","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":"89d945baf08000a074dfe30a407d938044e0cb785357745199f4096db5d8e47f","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2023-12-22T17:09:34Z","title_canon_sha256":"503bd45ba11381d8e018e25859ccbb98a605966696b6a95695805f5db92edcca"},"schema_version":"1.0","source":{"id":"2312.14836","kind":"arxiv","version":1}},"canonical_sha256":"10edee9adf3c5f36af1f2e10d3d4ffaee69e4381fd33c0cc89ef356a63a90305","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10edee9adf3c5f36af1f2e10d3d4ffaee69e4381fd33c0cc89ef356a63a90305","first_computed_at":"2026-07-05T07:27:20.507566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:27:20.507566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9fkzC8ejb702UHq7a8Lfwp6lXuD4OLKIAqq+2liA+Fg9JOzYKYbL6qOvMEVr2ojiIa+3Gi2cI27H0V+iQ7X/DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:27:20.508045Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.14836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1519c557ef90dc273ef781abc5f85b970acd1ca3f776a3596a0f30b0fc115d37","sha256:e0b11430598786315aaaf264faa79aee25c160cf39f0cbd2f76b70fa1e00fac2"],"state_sha256":"37d5f768ce8e8543dca1e5df2de99c1b1a1539393b87c04ab45bd70b0ac75b77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9PfBiBORGLrIk0NL+i+64SbxNPIzecOTgb0YS2uojHjrDBbj6Kbg7qNKmNTKTz86oxB9jVy5JAid+QwRje6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T08:52:43.944022Z","bundle_sha256":"4154b856c844786f2d6140f19141519a066e85a573e045d75ce20490d8a2d538"}}