{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U4LS6IR4AXURTOYCSBCWIRQUUF","short_pith_number":"pith:U4LS6IR4","canonical_record":{"source":{"id":"1111.4503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2011-11-18T21:46:32Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"e04047e8e2365f9ca044c4f51e6c53930d2724ccaa8cd0677e9e20a1f8c9d856","abstract_canon_sha256":"93bd6535e9f9d1242a22c8d9f2c6e642717e7a6a4b0eef8e4e5dd82d36c9218a"},"schema_version":"1.0"},"canonical_sha256":"a7172f223c05e919bb029045644614a1514ed9fb57bbe5a7a263baadd5b138d3","source":{"kind":"arxiv","id":"1111.4503","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4503","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4503v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4503","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"U4LS6IR4AXUR","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4LS6IR4AXURTOYC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4LS6IR4","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U4LS6IR4AXURTOYCSBCWIRQUUF","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2011-11-18T21:46:32Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"e04047e8e2365f9ca044c4f51e6c53930d2724ccaa8cd0677e9e20a1f8c9d856","abstract_canon_sha256":"93bd6535e9f9d1242a22c8d9f2c6e642717e7a6a4b0eef8e4e5dd82d36c9218a"},"schema_version":"1.0"},"canonical_sha256":"a7172f223c05e919bb029045644614a1514ed9fb57bbe5a7a263baadd5b138d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.173411Z","signature_b64":"bf9bRw2uFOniA8SpfePb3Kj7Ie2ZoMBCI86gi6Lr8gKF9aC12Y4yv/P/gZ2D2mFy11WMgPxOYCgtkVwlrPEMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7172f223c05e919bb029045644614a1514ed9fb57bbe5a7a263baadd5b138d3","last_reissued_at":"2026-05-18T04:08:03.172949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.172949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4503","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rL+egsQVrjburaz8KPYDs1uyJnwOvb2j8ZQYSiouopZ5PnZKJgMbruYl6UCVxmbAl+BV+Koatm3JZ9iOfblDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:25:31.840486Z"},"content_sha256":"40868fd71776e6facdbac4a8fa61a7e49f3ac38a585ec56a0b1ddd0a4dcf6d1a","schema_version":"1.0","event_id":"sha256:40868fd71776e6facdbac4a8fa61a7e49f3ac38a585ec56a0b1ddd0a4dcf6d1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U4LS6IR4AXURTOYCSBCWIRQUUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Anatomy of the Facebook Social Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Brian Karrer, Cameron Marlow, Johan Ugander, Lars Backstrom","submitted_at":"2011-11-18T21:46:32Z","abstract_excerpt":"We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the \"six degrees of separation\" phenomenon on a global scale. Sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4503","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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2/u0sfaD+TaH5tbo8qQSGQgZDadrX8pdsZA18MIo988NeiF6AK+h0rh/IdsPWN7h3D1ieLFBJ9a1N5v1gcjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:25:31.841130Z"},"content_sha256":"8890ac97429e28a5b3b920022be700af8420ba8d6da0f4cd8fa043783a7ee034","schema_version":"1.0","event_id":"sha256:8890ac97429e28a5b3b920022be700af8420ba8d6da0f4cd8fa043783a7ee034"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/bundle.json","state_url":"https://pith.science/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/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":"2026-05-31T21:25:31Z","links":{"resolver":"https://pith.science/pith/U4LS6IR4AXURTOYCSBCWIRQUUF","bundle":"https://pith.science/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/bundle.json","state":"https://pith.science/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4LS6IR4AXURTOYCSBCWIRQUUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U4LS6IR4AXURTOYCSBCWIRQUUF","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":"93bd6535e9f9d1242a22c8d9f2c6e642717e7a6a4b0eef8e4e5dd82d36c9218a","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2011-11-18T21:46:32Z","title_canon_sha256":"e04047e8e2365f9ca044c4f51e6c53930d2724ccaa8cd0677e9e20a1f8c9d856"},"schema_version":"1.0","source":{"id":"1111.4503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4503","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4503v1","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4503","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"U4LS6IR4AXUR","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4LS6IR4AXURTOYC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4LS6IR4","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:8890ac97429e28a5b3b920022be700af8420ba8d6da0f4cd8fa043783a7ee034","target":"graph","created_at":"2026-05-18T04:08:03Z","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":"We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single large connected component, and we confirm the \"six degrees of separation\" phenomenon on a global scale. Sec","authors_text":"Brian Karrer, Cameron Marlow, Johan Ugander, Lars Backstrom","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2011-11-18T21:46:32Z","title":"The Anatomy of the Facebook Social Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4503","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":"sha256:40868fd71776e6facdbac4a8fa61a7e49f3ac38a585ec56a0b1ddd0a4dcf6d1a","target":"record","created_at":"2026-05-18T04:08:03Z","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":"93bd6535e9f9d1242a22c8d9f2c6e642717e7a6a4b0eef8e4e5dd82d36c9218a","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2011-11-18T21:46:32Z","title_canon_sha256":"e04047e8e2365f9ca044c4f51e6c53930d2724ccaa8cd0677e9e20a1f8c9d856"},"schema_version":"1.0","source":{"id":"1111.4503","kind":"arxiv","version":1}},"canonical_sha256":"a7172f223c05e919bb029045644614a1514ed9fb57bbe5a7a263baadd5b138d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7172f223c05e919bb029045644614a1514ed9fb57bbe5a7a263baadd5b138d3","first_computed_at":"2026-05-18T04:08:03.172949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:03.172949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bf9bRw2uFOniA8SpfePb3Kj7Ie2ZoMBCI86gi6Lr8gKF9aC12Y4yv/P/gZ2D2mFy11WMgPxOYCgtkVwlrPEMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:03.173411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40868fd71776e6facdbac4a8fa61a7e49f3ac38a585ec56a0b1ddd0a4dcf6d1a","sha256:8890ac97429e28a5b3b920022be700af8420ba8d6da0f4cd8fa043783a7ee034"],"state_sha256":"f79e191f4c75e0c80213266e8dd1ead4a34a63316cb93a60d150a6818e48e52f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8tVJd0wrXoO1B/tCzK97zAH/ftDAAPW/tbJbZW6R1g7gJ8hCvzAHeBSL+D94wtGfCGeUZkowV3A59PaenGRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:25:31.844195Z","bundle_sha256":"9267c87e945fc1bf2a695c15440751f3d685cd6dc31a626be672447833b1a8f7"}}