{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VB7JU7M7Z3RNHAVMFLXBN6DSB5","short_pith_number":"pith:VB7JU7M7","canonical_record":{"source":{"id":"1907.03162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T17:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"997533f1dcddd915916d4b20f4fe80703630ec214f8fd9ece9ac28f409186558","abstract_canon_sha256":"06e6ffa902edb905b56c7475d9b01063f95dc141761ac9506ac4165c82158d73"},"schema_version":"1.0"},"canonical_sha256":"a87e9a7d9fcee2d382ac2aee16f8720f77ce94c6ccbddd6a0730ae6051d0139e","source":{"kind":"arxiv","id":"1907.03162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03162","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03162v1","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03162","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"VB7JU7M7Z3RN","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VB7JU7M7Z3RNHAVM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VB7JU7M7","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VB7JU7M7Z3RNHAVMFLXBN6DSB5","target":"record","payload":{"canonical_record":{"source":{"id":"1907.03162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T17:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"997533f1dcddd915916d4b20f4fe80703630ec214f8fd9ece9ac28f409186558","abstract_canon_sha256":"06e6ffa902edb905b56c7475d9b01063f95dc141761ac9506ac4165c82158d73"},"schema_version":"1.0"},"canonical_sha256":"a87e9a7d9fcee2d382ac2aee16f8720f77ce94c6ccbddd6a0730ae6051d0139e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:18.778088Z","signature_b64":"z1havsU/ikcUD4Uu4RvjidZ5kc4x+nSDnB85uSmlafhC29XmhcoRV5nXa0Sf8sJjcROZqPYsrrAaLyuhzUdGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a87e9a7d9fcee2d382ac2aee16f8720f77ce94c6ccbddd6a0730ae6051d0139e","last_reissued_at":"2026-05-17T23:41:18.777563Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:18.777563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.03162","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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKn7KOkiY2C5v79j1RafiWUhhWb6Uf4Q5xY6uyx496gFPbGOsp9IocKfnTEhlAYDQOz9PreDl+fGYsrYXYmOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:54:45.114520Z"},"content_sha256":"7a416c01bbc4840c909e02c5b2cd278b7d28b49caf6435766e4ffecf87f5f671","schema_version":"1.0","event_id":"sha256:7a416c01bbc4840c909e02c5b2cd278b7d28b49caf6435766e4ffecf87f5f671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VB7JU7M7Z3RNHAVMFLXBN6DSB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial separation algorithms for the continuous knapsack polyhedra with divisible capacities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Wei-Kun Chen, Yu-Hong Dai","submitted_at":"2019-07-06T17:43:50Z","abstract_excerpt":"It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the convex hulls of the sets which consist of $ n $ nonnegative integer variables, one unbounded continuous, $ m $ bounded continuous variables, and one linear constraint in either $ \\geq $ or $ \\leq $ form where the coefficients of integer variables are integer and divisible. Wolsey and Yaman (Math Program 156: 1--20, 2016) have shown that the polyhedra can be des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03162","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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHduvk5TazgiI4H5CWPi0f5zoK7bYW0C7gUT4hchwaPxmqtkIpQV5/Z+nXZqHPie/anWFJwnczJ69F2OY+e0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:54:45.114995Z"},"content_sha256":"2aef202f8ecc60f79b8158816a04181ccdf4328faf7a374bc055b4440d306163","schema_version":"1.0","event_id":"sha256:2aef202f8ecc60f79b8158816a04181ccdf4328faf7a374bc055b4440d306163"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/bundle.json","state_url":"https://pith.science/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/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":"2026-05-18T21:54:45Z","links":{"resolver":"https://pith.science/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5","bundle":"https://pith.science/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/bundle.json","state":"https://pith.science/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB7JU7M7Z3RNHAVMFLXBN6DSB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VB7JU7M7Z3RNHAVMFLXBN6DSB5","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":"06e6ffa902edb905b56c7475d9b01063f95dc141761ac9506ac4165c82158d73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T17:43:50Z","title_canon_sha256":"997533f1dcddd915916d4b20f4fe80703630ec214f8fd9ece9ac28f409186558"},"schema_version":"1.0","source":{"id":"1907.03162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03162","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03162v1","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03162","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"VB7JU7M7Z3RN","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VB7JU7M7Z3RNHAVM","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VB7JU7M7","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2aef202f8ecc60f79b8158816a04181ccdf4328faf7a374bc055b4440d306163","target":"graph","created_at":"2026-05-17T23:41:18Z","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":"It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the convex hulls of the sets which consist of $ n $ nonnegative integer variables, one unbounded continuous, $ m $ bounded continuous variables, and one linear constraint in either $ \\geq $ or $ \\leq $ form where the coefficients of integer variables are integer and divisible. Wolsey and Yaman (Math Program 156: 1--20, 2016) have shown that the polyhedra can be des","authors_text":"Wei-Kun Chen, Yu-Hong Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T17:43:50Z","title":"Combinatorial separation algorithms for the continuous knapsack polyhedra with divisible capacities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03162","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":"sha256:7a416c01bbc4840c909e02c5b2cd278b7d28b49caf6435766e4ffecf87f5f671","target":"record","created_at":"2026-05-17T23:41:18Z","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":"06e6ffa902edb905b56c7475d9b01063f95dc141761ac9506ac4165c82158d73","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T17:43:50Z","title_canon_sha256":"997533f1dcddd915916d4b20f4fe80703630ec214f8fd9ece9ac28f409186558"},"schema_version":"1.0","source":{"id":"1907.03162","kind":"arxiv","version":1}},"canonical_sha256":"a87e9a7d9fcee2d382ac2aee16f8720f77ce94c6ccbddd6a0730ae6051d0139e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a87e9a7d9fcee2d382ac2aee16f8720f77ce94c6ccbddd6a0730ae6051d0139e","first_computed_at":"2026-05-17T23:41:18.777563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:18.777563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z1havsU/ikcUD4Uu4RvjidZ5kc4x+nSDnB85uSmlafhC29XmhcoRV5nXa0Sf8sJjcROZqPYsrrAaLyuhzUdGBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:18.778088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a416c01bbc4840c909e02c5b2cd278b7d28b49caf6435766e4ffecf87f5f671","sha256:2aef202f8ecc60f79b8158816a04181ccdf4328faf7a374bc055b4440d306163"],"state_sha256":"21f4cb3ffe52a1b383d81519ef530002924fbfc0297b2746a7eccf1477f474bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x6gumn06a+3GsBpUt0x81HfgbwJZyDyQRJ4oi/r2TXhDz12MBx09y3iSUbdIIsUhyqo/goSCEom4X4zcnBgaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:54:45.117130Z","bundle_sha256":"2c47e2aee0c8ec5459607d8c982e859d46832a49d1350fcf06bc1c74faeda3b7"}}