{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P47PWCW2IH6A2FVEXOQO4N53Z4","short_pith_number":"pith:P47PWCW2","canonical_record":{"source":{"id":"1908.06541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-19T00:12:06Z","cross_cats_sorted":["math.CO","math.OC"],"title_canon_sha256":"43e1c14f122e51e6ed6aa1c8e3ff343400f8bcd7ecbde9e675a0c5d5586025fe","abstract_canon_sha256":"b0a4cae1a49de08d711bc7b57f96c049ac475655d7f056397f246496f5bdb521"},"schema_version":"1.0"},"canonical_sha256":"7f3efb0ada41fc0d16a4bba0ee37bbcf257b6794a026405bf6cf60940934077b","source":{"kind":"arxiv","id":"1908.06541","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06541","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06541v2","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06541","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_12","alias_value":"P47PWCW2IH6A","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_16","alias_value":"P47PWCW2IH6A2FVE","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_8","alias_value":"P47PWCW2","created_at":"2026-07-04T23:58:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P47PWCW2IH6A2FVEXOQO4N53Z4","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-19T00:12:06Z","cross_cats_sorted":["math.CO","math.OC"],"title_canon_sha256":"43e1c14f122e51e6ed6aa1c8e3ff343400f8bcd7ecbde9e675a0c5d5586025fe","abstract_canon_sha256":"b0a4cae1a49de08d711bc7b57f96c049ac475655d7f056397f246496f5bdb521"},"schema_version":"1.0"},"canonical_sha256":"7f3efb0ada41fc0d16a4bba0ee37bbcf257b6794a026405bf6cf60940934077b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:29.378969Z","signature_b64":"zmquLrOzgU4HJY+WGqAnxdSRsjNl77CJxwhGH/h9H3/UZhV5hXs5xI13qzPwsTA0oK976MlhL36Hs8XXFhduBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f3efb0ada41fc0d16a4bba0ee37bbcf257b6794a026405bf6cf60940934077b","last_reissued_at":"2026-07-04T23:58:29.378588Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:29.378588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06541","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:58:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqwoBT+aajJD/314REbBGb/Gi37wc5JDL+xbmNkJf5GNJ87yel5e8nbTmRfFiunhvf1P8FJU/br/A6236VuqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:49:30.760686Z"},"content_sha256":"05e34fa353e183441c3c54042fd232531bd2345f0e8b7267be6f1244cad176a6","schema_version":"1.0","event_id":"sha256:05e34fa353e183441c3c54042fd232531bd2345f0e8b7267be6f1244cad176a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P47PWCW2IH6A2FVEXOQO4N53Z4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Landscape of Minimum Label Cut (Hedge Connectivity) Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC"],"primary_cat":"cs.DS","authors_text":"Andr\\'as Farag\\'o, Rupei Xu","submitted_at":"2019-08-19T00:12:06Z","abstract_excerpt":"Minimum Label Cut (or Hedge Connectivity) problem is defined as follows: given an undirected graph $G=(V, E)$ with $n$ vertices and $m$ edges, in which, each edge is labeled (with one or multiple labels) from a label set $L=\\{\\ell_1,\\ell_2, ..., \\ell_{|L|}\\}$, the edges may be weighted with weight set $W =\\{w_1, w_2, ..., w_m\\}$, the label cut problem(hedge connectivity) problem asks for the minimum number of edge sets(each edge set (or hedge) is the edges with the same label) whose removal disconnects the source-sink pair of vertices or the whole graph with minimum total weights(minimum cardi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06541","kind":"arxiv","version":2},"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/1908.06541/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":"2026-07-04T23:58:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tSUXOZkxtbJp5ij7yf7c2k1cVUm1nDr0yVkz5X7brPnczY0WjKTtku6xt9yRrgWODAJz8MZznyuKWcACnrqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:49:30.761301Z"},"content_sha256":"68b3d2b0443559e92fea17c8623b39e4528630ee7557315baf79ca7ef5d71254","schema_version":"1.0","event_id":"sha256:68b3d2b0443559e92fea17c8623b39e4528630ee7557315baf79ca7ef5d71254"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/bundle.json","state_url":"https://pith.science/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/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":"2026-08-16T10:49:30Z","links":{"resolver":"https://pith.science/pith/P47PWCW2IH6A2FVEXOQO4N53Z4","bundle":"https://pith.science/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/bundle.json","state":"https://pith.science/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P47PWCW2IH6A2FVEXOQO4N53Z4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P47PWCW2IH6A2FVEXOQO4N53Z4","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":"b0a4cae1a49de08d711bc7b57f96c049ac475655d7f056397f246496f5bdb521","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-19T00:12:06Z","title_canon_sha256":"43e1c14f122e51e6ed6aa1c8e3ff343400f8bcd7ecbde9e675a0c5d5586025fe"},"schema_version":"1.0","source":{"id":"1908.06541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06541","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06541v2","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06541","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_12","alias_value":"P47PWCW2IH6A","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_16","alias_value":"P47PWCW2IH6A2FVE","created_at":"2026-07-04T23:58:29Z"},{"alias_kind":"pith_short_8","alias_value":"P47PWCW2","created_at":"2026-07-04T23:58:29Z"}],"graph_snapshots":[{"event_id":"sha256:68b3d2b0443559e92fea17c8623b39e4528630ee7557315baf79ca7ef5d71254","target":"graph","created_at":"2026-07-04T23:58:29Z","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/1908.06541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Minimum Label Cut (or Hedge Connectivity) problem is defined as follows: given an undirected graph $G=(V, E)$ with $n$ vertices and $m$ edges, in which, each edge is labeled (with one or multiple labels) from a label set $L=\\{\\ell_1,\\ell_2, ..., \\ell_{|L|}\\}$, the edges may be weighted with weight set $W =\\{w_1, w_2, ..., w_m\\}$, the label cut problem(hedge connectivity) problem asks for the minimum number of edge sets(each edge set (or hedge) is the edges with the same label) whose removal disconnects the source-sink pair of vertices or the whole graph with minimum total weights(minimum cardi","authors_text":"Andr\\'as Farag\\'o, Rupei Xu","cross_cats":["math.CO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-19T00:12:06Z","title":"The Landscape of Minimum Label Cut (Hedge Connectivity) Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06541","kind":"arxiv","version":2},"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":"sha256:05e34fa353e183441c3c54042fd232531bd2345f0e8b7267be6f1244cad176a6","target":"record","created_at":"2026-07-04T23:58:29Z","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":"b0a4cae1a49de08d711bc7b57f96c049ac475655d7f056397f246496f5bdb521","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-19T00:12:06Z","title_canon_sha256":"43e1c14f122e51e6ed6aa1c8e3ff343400f8bcd7ecbde9e675a0c5d5586025fe"},"schema_version":"1.0","source":{"id":"1908.06541","kind":"arxiv","version":2}},"canonical_sha256":"7f3efb0ada41fc0d16a4bba0ee37bbcf257b6794a026405bf6cf60940934077b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f3efb0ada41fc0d16a4bba0ee37bbcf257b6794a026405bf6cf60940934077b","first_computed_at":"2026-07-04T23:58:29.378588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:29.378588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zmquLrOzgU4HJY+WGqAnxdSRsjNl77CJxwhGH/h9H3/UZhV5hXs5xI13qzPwsTA0oK976MlhL36Hs8XXFhduBA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:29.378969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05e34fa353e183441c3c54042fd232531bd2345f0e8b7267be6f1244cad176a6","sha256:68b3d2b0443559e92fea17c8623b39e4528630ee7557315baf79ca7ef5d71254"],"state_sha256":"61b48adf7c7c33e04e7fe3738206bc9233e168cd3a7c4d417272c9a1873e71ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ao/4UCWwnRF/3NxxvvFYR4OY5aPYMOmeaFuFa//GhVnvfT3Kalc3+v4zuOuOHnNH30qb1mpjk1k5h9efTfpSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:49:30.766701Z","bundle_sha256":"fa55e8556cb5f8acb019bd1a746544137daf210e10bf84a6f648ceb37c01c2b0"}}