{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IPQOA2NZFVXDKJC23EWJL733O6","short_pith_number":"pith:IPQOA2NZ","canonical_record":{"source":{"id":"1704.03913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-04-12T19:48:31Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"title_canon_sha256":"3d7238ee900ce795668367dec92cb7a637f23bc329a22297c318a0fe9051ff64","abstract_canon_sha256":"1243571e067ed8797a89b91ace1f7e81fe8746fa8f2148467e48636b22d0fe5f"},"schema_version":"1.0"},"canonical_sha256":"43e0e069b92d6e35245ad92c95ff7b7784201a1841ea475ab038010fe131c350","source":{"kind":"arxiv","id":"1704.03913","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03913","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03913v2","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03913","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"IPQOA2NZFVXD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IPQOA2NZFVXDKJC2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IPQOA2NZ","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IPQOA2NZFVXDKJC23EWJL733O6","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-04-12T19:48:31Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"title_canon_sha256":"3d7238ee900ce795668367dec92cb7a637f23bc329a22297c318a0fe9051ff64","abstract_canon_sha256":"1243571e067ed8797a89b91ace1f7e81fe8746fa8f2148467e48636b22d0fe5f"},"schema_version":"1.0"},"canonical_sha256":"43e0e069b92d6e35245ad92c95ff7b7784201a1841ea475ab038010fe131c350","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:24.321046Z","signature_b64":"sGfMnVqSuyUrtCLE5ShUuDQ8TAtg8lf81DQ4fB0ra/HU4NeNHwFq4jmMwSj3lTDKUT1DGFQwbk05z6HZb1vvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43e0e069b92d6e35245ad92c95ff7b7784201a1841ea475ab038010fe131c350","last_reissued_at":"2026-05-18T00:15:24.320337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:24.320337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03913","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":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmStjzGesWYsJTH84m2SYUZaBf64xOw5/w439lzMD1gj+2YSx38CVAhw4o02T+nm8Xxd1GNrb+f0hEqqVAWEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:50:47.296815Z"},"content_sha256":"a2414eff404f57a1bf42f5dd631772e92a37c4d1ef2ffda066bbbafab3a401f8","schema_version":"1.0","event_id":"sha256:a2414eff404f57a1bf42f5dd631772e92a37c4d1ef2ffda066bbbafab3a401f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IPQOA2NZFVXDKJC23EWJL733O6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-order clustering in networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"primary_cat":"cs.SI","authors_text":"Austin R. Benson, Hao Yin, Jure Leskovec","submitted_at":"2017-04-12T19:48:31Z","abstract_excerpt":"A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03913","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":""},"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":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLb5coG9dMfUGvkE4+AaJh47M0LfsVJyblPLRdqIPbNJx3junCQwAjLH9c4wibFkwZVtKBvPVUBI6+LUfLDNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:50:47.297501Z"},"content_sha256":"d72a938ec106c823add49f2ff511853eadc8b757eb21991bb2585c9ceaba34ee","schema_version":"1.0","event_id":"sha256:d72a938ec106c823add49f2ff511853eadc8b757eb21991bb2585c9ceaba34ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPQOA2NZFVXDKJC23EWJL733O6/bundle.json","state_url":"https://pith.science/pith/IPQOA2NZFVXDKJC23EWJL733O6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPQOA2NZFVXDKJC23EWJL733O6/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":"2026-05-31T11:50:47Z","links":{"resolver":"https://pith.science/pith/IPQOA2NZFVXDKJC23EWJL733O6","bundle":"https://pith.science/pith/IPQOA2NZFVXDKJC23EWJL733O6/bundle.json","state":"https://pith.science/pith/IPQOA2NZFVXDKJC23EWJL733O6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPQOA2NZFVXDKJC23EWJL733O6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IPQOA2NZFVXDKJC23EWJL733O6","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":"1243571e067ed8797a89b91ace1f7e81fe8746fa8f2148467e48636b22d0fe5f","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-04-12T19:48:31Z","title_canon_sha256":"3d7238ee900ce795668367dec92cb7a637f23bc329a22297c318a0fe9051ff64"},"schema_version":"1.0","source":{"id":"1704.03913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03913","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03913v2","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03913","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"IPQOA2NZFVXD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IPQOA2NZFVXDKJC2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IPQOA2NZ","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:d72a938ec106c823add49f2ff511853eadc8b757eb21991bb2585c9ceaba34ee","target":"graph","created_at":"2026-05-18T00:15:24Z","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":"A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a ","authors_text":"Austin R. Benson, Hao Yin, Jure Leskovec","cross_cats":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-04-12T19:48:31Z","title":"Higher-order clustering in networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03913","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:a2414eff404f57a1bf42f5dd631772e92a37c4d1ef2ffda066bbbafab3a401f8","target":"record","created_at":"2026-05-18T00:15:24Z","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":"1243571e067ed8797a89b91ace1f7e81fe8746fa8f2148467e48636b22d0fe5f","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-04-12T19:48:31Z","title_canon_sha256":"3d7238ee900ce795668367dec92cb7a637f23bc329a22297c318a0fe9051ff64"},"schema_version":"1.0","source":{"id":"1704.03913","kind":"arxiv","version":2}},"canonical_sha256":"43e0e069b92d6e35245ad92c95ff7b7784201a1841ea475ab038010fe131c350","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43e0e069b92d6e35245ad92c95ff7b7784201a1841ea475ab038010fe131c350","first_computed_at":"2026-05-18T00:15:24.320337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:24.320337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sGfMnVqSuyUrtCLE5ShUuDQ8TAtg8lf81DQ4fB0ra/HU4NeNHwFq4jmMwSj3lTDKUT1DGFQwbk05z6HZb1vvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:24.321046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2414eff404f57a1bf42f5dd631772e92a37c4d1ef2ffda066bbbafab3a401f8","sha256:d72a938ec106c823add49f2ff511853eadc8b757eb21991bb2585c9ceaba34ee"],"state_sha256":"9fd626ae2daf948d5f70168de9d17d46f56cf4760edf9f8a7b28cc4816c0818d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0D3KEgLHH1MP85AN/Y2pKNdC33HhjnlgVJlQZ1mqO7DSsXWMmEWfyiPXpE62YYxQGfNGF1iMt7eVLzgy0SECAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:50:47.300933Z","bundle_sha256":"1d9cd3fbfd138a8f2d89677bbd51e26f420b9fe64a8aa235aafebd37e0f5f4ac"}}