{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H6W64PN5ETB5CKCIXU5WNSRL3F","short_pith_number":"pith:H6W64PN5","canonical_record":{"source":{"id":"1812.00283","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-01T23:19:53Z","cross_cats_sorted":[],"title_canon_sha256":"f15258e4d861d318a439f4e81d912c3f6c4a7555a794d7c56faad0bac6a45e6b","abstract_canon_sha256":"175dc6fc55f92f66660be4096a74364a4cfb85e8c3ef8c8bcdbdafe3297f46e3"},"schema_version":"1.0"},"canonical_sha256":"3fadee3dbd24c3d12848bd3b66ca2bd9431b101fff21dba0d7a368f104665bb3","source":{"kind":"arxiv","id":"1812.00283","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00283","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00283v3","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00283","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"H6W64PN5ETB5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6W64PN5ETB5CKCI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6W64PN5","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H6W64PN5ETB5CKCIXU5WNSRL3F","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00283","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-01T23:19:53Z","cross_cats_sorted":[],"title_canon_sha256":"f15258e4d861d318a439f4e81d912c3f6c4a7555a794d7c56faad0bac6a45e6b","abstract_canon_sha256":"175dc6fc55f92f66660be4096a74364a4cfb85e8c3ef8c8bcdbdafe3297f46e3"},"schema_version":"1.0"},"canonical_sha256":"3fadee3dbd24c3d12848bd3b66ca2bd9431b101fff21dba0d7a368f104665bb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:08.517544Z","signature_b64":"8NwKeB6Me8w9bVrEcGa/EqmPbioru3wkluFU/rJui84z+pr6lG9dCYd0GoohoiJw30DgbwHW9qh5fGyfYsjwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fadee3dbd24c3d12848bd3b66ca2bd9431b101fff21dba0d7a368f104665bb3","last_reissued_at":"2026-05-17T23:42:08.517059Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:08.517059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00283","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":"2026-05-17T23:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1SJSlRg/uZ4piyBGYr4aW4wNZIH+2edZx17kmYAwCXyNH1RSPPy95bSbv2E0xYM2mi5vUgzA7BPVnbFUoWDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:39:37.749444Z"},"content_sha256":"e8cd7e81cd23176f32df3881baa78b39a6d882cd0a546d975e678b0723b0f1dc","schema_version":"1.0","event_id":"sha256:e8cd7e81cd23176f32df3881baa78b39a6d882cd0a546d975e678b0723b0f1dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H6W64PN5ETB5CKCIXU5WNSRL3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Butterfly Counting for Large Bipartite Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Kai Wang, Lu Qin, Wenjie Zhang, Xuemin Lin, Ying Zhang","submitted_at":"2018-12-01T23:19:53Z","abstract_excerpt":"Bipartite networks are of great importance in many real-world applications. In bipartite networks, butterfly (i.e., a complete 2 x 2 biclique) is the smallest non-trivial cohesive structure and plays a key role. In this paper, we study the problem of efficient counting the number of butterflies in bipartite networks. The most advanced techniques are based on enumerating wedges which is the dominant cost of counting butterflies. Nevertheless, the existing algorithms cannot efficiently handle large-scale bipartite networks. This becomes a bottleneck in large-scale applications. In this paper, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00283","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":""},"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":"2026-05-17T23:42:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ddLjkfc6PMY9MOooF4VkQnawRCHT/YyGCj31E54VAy9a31s091J0cag2S+AjfHGTHSQLedISbDwXSwyUGk5SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:39:37.750077Z"},"content_sha256":"95a74be8515941aba7fbdd293f84731419cea85cea2be2ccaec0703903a9eb7f","schema_version":"1.0","event_id":"sha256:95a74be8515941aba7fbdd293f84731419cea85cea2be2ccaec0703903a9eb7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/bundle.json","state_url":"https://pith.science/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/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":"2026-05-30T19:39:37Z","links":{"resolver":"https://pith.science/pith/H6W64PN5ETB5CKCIXU5WNSRL3F","bundle":"https://pith.science/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/bundle.json","state":"https://pith.science/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6W64PN5ETB5CKCIXU5WNSRL3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H6W64PN5ETB5CKCIXU5WNSRL3F","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":"175dc6fc55f92f66660be4096a74364a4cfb85e8c3ef8c8bcdbdafe3297f46e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-01T23:19:53Z","title_canon_sha256":"f15258e4d861d318a439f4e81d912c3f6c4a7555a794d7c56faad0bac6a45e6b"},"schema_version":"1.0","source":{"id":"1812.00283","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00283","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00283v3","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00283","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"H6W64PN5ETB5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6W64PN5ETB5CKCI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6W64PN5","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:95a74be8515941aba7fbdd293f84731419cea85cea2be2ccaec0703903a9eb7f","target":"graph","created_at":"2026-05-17T23:42:08Z","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":"Bipartite networks are of great importance in many real-world applications. In bipartite networks, butterfly (i.e., a complete 2 x 2 biclique) is the smallest non-trivial cohesive structure and plays a key role. In this paper, we study the problem of efficient counting the number of butterflies in bipartite networks. The most advanced techniques are based on enumerating wedges which is the dominant cost of counting butterflies. Nevertheless, the existing algorithms cannot efficiently handle large-scale bipartite networks. This becomes a bottleneck in large-scale applications. In this paper, in","authors_text":"Kai Wang, Lu Qin, Wenjie Zhang, Xuemin Lin, Ying Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-01T23:19:53Z","title":"Efficient Butterfly Counting for Large Bipartite Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00283","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:e8cd7e81cd23176f32df3881baa78b39a6d882cd0a546d975e678b0723b0f1dc","target":"record","created_at":"2026-05-17T23:42:08Z","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":"175dc6fc55f92f66660be4096a74364a4cfb85e8c3ef8c8bcdbdafe3297f46e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2018-12-01T23:19:53Z","title_canon_sha256":"f15258e4d861d318a439f4e81d912c3f6c4a7555a794d7c56faad0bac6a45e6b"},"schema_version":"1.0","source":{"id":"1812.00283","kind":"arxiv","version":3}},"canonical_sha256":"3fadee3dbd24c3d12848bd3b66ca2bd9431b101fff21dba0d7a368f104665bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fadee3dbd24c3d12848bd3b66ca2bd9431b101fff21dba0d7a368f104665bb3","first_computed_at":"2026-05-17T23:42:08.517059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:08.517059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8NwKeB6Me8w9bVrEcGa/EqmPbioru3wkluFU/rJui84z+pr6lG9dCYd0GoohoiJw30DgbwHW9qh5fGyfYsjwDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:08.517544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00283","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8cd7e81cd23176f32df3881baa78b39a6d882cd0a546d975e678b0723b0f1dc","sha256:95a74be8515941aba7fbdd293f84731419cea85cea2be2ccaec0703903a9eb7f"],"state_sha256":"9e256f46efadd1f460e4072899d45d764ac9b2ad89f2629fb54949c90f29479c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gY4e6Zotf4LDmwTIP08VsD3MAlJKjvWD3qucG2saAE7B3u+ra4sMwnjrQgPltR4Eo6/DWXYGFLOLPzKOCJliAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:39:37.753291Z","bundle_sha256":"ba01ce3dddd80d0bf89edf9bddfc2916829865bb4c2f2f2e339235dd53ab1c0b"}}