{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QW5KLNZ2SUET7OBKR7IMDEGKWK","short_pith_number":"pith:QW5KLNZ2","canonical_record":{"source":{"id":"2407.00312","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-06-29T04:29:03Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"b4ee935010cd310897d0cf75d50a39b1030084ff5f4d68fd2f14a41cd59737ee","abstract_canon_sha256":"b24ea848a9930805e23a7b3b4b02f36ca15466615cf58e3233c258514a3d3a27"},"schema_version":"1.0"},"canonical_sha256":"85baa5b73a95093fb82a8fd0c190cab29b2cf12f560779beb15ec2cbfc83042f","source":{"kind":"arxiv","id":"2407.00312","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.00312","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.00312v4","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.00312","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"QW5KLNZ2SUET","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_16","alias_value":"QW5KLNZ2SUET7OBK","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_8","alias_value":"QW5KLNZ2","created_at":"2026-07-05T10:02:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QW5KLNZ2SUET7OBKR7IMDEGKWK","target":"record","payload":{"canonical_record":{"source":{"id":"2407.00312","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-06-29T04:29:03Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"b4ee935010cd310897d0cf75d50a39b1030084ff5f4d68fd2f14a41cd59737ee","abstract_canon_sha256":"b24ea848a9930805e23a7b3b4b02f36ca15466615cf58e3233c258514a3d3a27"},"schema_version":"1.0"},"canonical_sha256":"85baa5b73a95093fb82a8fd0c190cab29b2cf12f560779beb15ec2cbfc83042f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:23.576936Z","signature_b64":"hVS9XgEfpsijV/spEFSEDNmcmXbaVmhO4T9ltM0APkrZUFj1fY6i0IPx9SrBBdN6YAzr3igQwPaE+VpcOaIUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85baa5b73a95093fb82a8fd0c190cab29b2cf12f560779beb15ec2cbfc83042f","last_reissued_at":"2026-07-05T10:02:23.576514Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:23.576514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.00312","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6dCCiUC+TcCsCeOl1PiFHEi33RlhVXSVzmXAcY+Ed0ZUR/s5uZcotCxatyDdKhrzdQ8/QaNr6g2F9qlo/soDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:33:48.551203Z"},"content_sha256":"9b727d0bcbd076ffc430eb156ce736f7bc1059126ec50db75f8da024884ba2e2","schema_version":"1.0","event_id":"sha256:9b727d0bcbd076ffc430eb156ce736f7bc1059126ec50db75f8da024884ba2e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QW5KLNZ2SUET7OBKR7IMDEGKWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE"],"primary_cat":"cs.AI","authors_text":"Changliang Zhou, Mingxuan Yuan, Tong Xialiang, Zhenkun Wang, Zhi Zheng","submitted_at":"2024-06-29T04:29:03Z","abstract_excerpt":"Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.00312","kind":"arxiv","version":4},"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/2407.00312/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":"2026-07-05T10:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ed6lMrtQvRHkqfSFPwSmpg8XyfGG+vp+/ldITYe6TDtNZ8sWkfoJSTAkXZjq/d9PRavAi9JKP4O8RJSDXJxKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:33:48.551588Z"},"content_sha256":"e38119ad333955ddfbe5fd02e341033271de758f52a0f7cf621171b6f46e0115","schema_version":"1.0","event_id":"sha256:e38119ad333955ddfbe5fd02e341033271de758f52a0f7cf621171b6f46e0115"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/bundle.json","state_url":"https://pith.science/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/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":"2026-08-20T08:33:48Z","links":{"resolver":"https://pith.science/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK","bundle":"https://pith.science/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/bundle.json","state":"https://pith.science/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QW5KLNZ2SUET7OBKR7IMDEGKWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QW5KLNZ2SUET7OBKR7IMDEGKWK","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":"b24ea848a9930805e23a7b3b4b02f36ca15466615cf58e3233c258514a3d3a27","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-06-29T04:29:03Z","title_canon_sha256":"b4ee935010cd310897d0cf75d50a39b1030084ff5f4d68fd2f14a41cd59737ee"},"schema_version":"1.0","source":{"id":"2407.00312","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.00312","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"2407.00312v4","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.00312","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"QW5KLNZ2SUET","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_16","alias_value":"QW5KLNZ2SUET7OBK","created_at":"2026-07-05T10:02:23Z"},{"alias_kind":"pith_short_8","alias_value":"QW5KLNZ2","created_at":"2026-07-05T10:02:23Z"}],"graph_snapshots":[{"event_id":"sha256:e38119ad333955ddfbe5fd02e341033271de758f52a0f7cf621171b6f46e0115","target":"graph","created_at":"2026-07-05T10:02:23Z","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/2407.00312/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their ","authors_text":"Changliang Zhou, Mingxuan Yuan, Tong Xialiang, Zhenkun Wang, Zhi Zheng","cross_cats":["cs.NE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-06-29T04:29:03Z","title":"UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.00312","kind":"arxiv","version":4},"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":"sha256:9b727d0bcbd076ffc430eb156ce736f7bc1059126ec50db75f8da024884ba2e2","target":"record","created_at":"2026-07-05T10:02:23Z","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":"b24ea848a9930805e23a7b3b4b02f36ca15466615cf58e3233c258514a3d3a27","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2024-06-29T04:29:03Z","title_canon_sha256":"b4ee935010cd310897d0cf75d50a39b1030084ff5f4d68fd2f14a41cd59737ee"},"schema_version":"1.0","source":{"id":"2407.00312","kind":"arxiv","version":4}},"canonical_sha256":"85baa5b73a95093fb82a8fd0c190cab29b2cf12f560779beb15ec2cbfc83042f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85baa5b73a95093fb82a8fd0c190cab29b2cf12f560779beb15ec2cbfc83042f","first_computed_at":"2026-07-05T10:02:23.576514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:23.576514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hVS9XgEfpsijV/spEFSEDNmcmXbaVmhO4T9ltM0APkrZUFj1fY6i0IPx9SrBBdN6YAzr3igQwPaE+VpcOaIUDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:23.576936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.00312","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b727d0bcbd076ffc430eb156ce736f7bc1059126ec50db75f8da024884ba2e2","sha256:e38119ad333955ddfbe5fd02e341033271de758f52a0f7cf621171b6f46e0115"],"state_sha256":"e0602ed999eebd2940fe28a9d38e32564808a6f26340d89f98934ea054c444ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBouFOdzxHJIis6btyp1nJ6G3GgpfqrZj1ZSPnHzwyiZBkHJd7YklgeuwKNe1seLBOYIdxDgPyLRuqFlKFlMBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T08:33:48.554003Z","bundle_sha256":"bc4c29caf0227c8d56a50c6033b86ad35443967f329c613bfc818169d45330cf"}}