{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:S7SFZK7HANVDQOI44ER44CDYF2","short_pith_number":"pith:S7SFZK7H","canonical_record":{"source":{"id":"1405.0157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-05-01T13:19:58Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"6482a484bc019f8cdb472cfec802baffa91eaad80735abf1ce7162f6aa1227d2","abstract_canon_sha256":"53527e69181aa27cb1be74591023d3a4b0129429415a0d56c58de6df4f238416"},"schema_version":"1.0"},"canonical_sha256":"97e45cabe7036a38391ce123ce08782e8408b75181e7232b4a4a3097c42386ca","source":{"kind":"arxiv","id":"1405.0157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0157","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0157v1","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0157","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"S7SFZK7HANVD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S7SFZK7HANVDQOI4","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S7SFZK7H","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:S7SFZK7HANVDQOI44ER44CDYF2","target":"record","payload":{"canonical_record":{"source":{"id":"1405.0157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-05-01T13:19:58Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"6482a484bc019f8cdb472cfec802baffa91eaad80735abf1ce7162f6aa1227d2","abstract_canon_sha256":"53527e69181aa27cb1be74591023d3a4b0129429415a0d56c58de6df4f238416"},"schema_version":"1.0"},"canonical_sha256":"97e45cabe7036a38391ce123ce08782e8408b75181e7232b4a4a3097c42386ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:21.066887Z","signature_b64":"dLRxAOMtvwgshispUyI1UVFtu+5gNpEmHc2/A7pga6Uf9L88wGB17A8SeU00+2Hpj5+FMxv+aG5JlecwhmIuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e45cabe7036a38391ce123ce08782e8408b75181e7232b4a4a3097c42386ca","last_reissued_at":"2026-05-18T01:43:21.066387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:21.066387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.0157","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":"2026-05-18T01:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9eZXf2jTuX94umsTgPbaQkqxD6UmkVCZLGe0uqzGCGwgQuyx34t8erT/ilaSffEvJrzYMUyb3s9W16n2tJ+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:46:17.440196Z"},"content_sha256":"f78884404457c84e8802efc1476773fd9d08853ebbed3c36205d942d29f5916d","schema_version":"1.0","event_id":"sha256:f78884404457c84e8802efc1476773fd9d08853ebbed3c36205d942d29f5916d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:S7SFZK7HANVDQOI44ER44CDYF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensionality of social networks using motifs and eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Amanda Tian, Anthony Bonato, David F. Gleich, Dieter Mitsche, Myunghwan Kim, Pawe{\\l} Pra{\\l}at, Stephen J. Young","submitted_at":"2014-05-01T13:19:58Z","abstract_excerpt":"We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when $m$ scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0157","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":"2026-05-18T01:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OI8D4IN2/Li+qeMANPBq7lF+zBJPtykaBF1iM6cpKZuf6jyA7AqeKkrHnb1TCdszCy9tXYE015C1qW/CYmVADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:46:17.440553Z"},"content_sha256":"7ed97e66fe3a0902c50c5e132bac269f399cabf3e472f5a9ab9a06190cd2cad5","schema_version":"1.0","event_id":"sha256:7ed97e66fe3a0902c50c5e132bac269f399cabf3e472f5a9ab9a06190cd2cad5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7SFZK7HANVDQOI44ER44CDYF2/bundle.json","state_url":"https://pith.science/pith/S7SFZK7HANVDQOI44ER44CDYF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7SFZK7HANVDQOI44ER44CDYF2/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":"2026-06-25T09:46:17Z","links":{"resolver":"https://pith.science/pith/S7SFZK7HANVDQOI44ER44CDYF2","bundle":"https://pith.science/pith/S7SFZK7HANVDQOI44ER44CDYF2/bundle.json","state":"https://pith.science/pith/S7SFZK7HANVDQOI44ER44CDYF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7SFZK7HANVDQOI44ER44CDYF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S7SFZK7HANVDQOI44ER44CDYF2","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":"53527e69181aa27cb1be74591023d3a4b0129429415a0d56c58de6df4f238416","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-05-01T13:19:58Z","title_canon_sha256":"6482a484bc019f8cdb472cfec802baffa91eaad80735abf1ce7162f6aa1227d2"},"schema_version":"1.0","source":{"id":"1405.0157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0157","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0157v1","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0157","created_at":"2026-05-18T01:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"S7SFZK7HANVD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S7SFZK7HANVDQOI4","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S7SFZK7H","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:7ed97e66fe3a0902c50c5e132bac269f399cabf3e472f5a9ab9a06190cd2cad5","target":"graph","created_at":"2026-05-18T01:43:21Z","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 consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an $m$-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when $m$ scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the di","authors_text":"Amanda Tian, Anthony Bonato, David F. Gleich, Dieter Mitsche, Myunghwan Kim, Pawe{\\l} Pra{\\l}at, Stephen J. Young","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-05-01T13:19:58Z","title":"Dimensionality of social networks using motifs and eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0157","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:f78884404457c84e8802efc1476773fd9d08853ebbed3c36205d942d29f5916d","target":"record","created_at":"2026-05-18T01:43:21Z","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":"53527e69181aa27cb1be74591023d3a4b0129429415a0d56c58de6df4f238416","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-05-01T13:19:58Z","title_canon_sha256":"6482a484bc019f8cdb472cfec802baffa91eaad80735abf1ce7162f6aa1227d2"},"schema_version":"1.0","source":{"id":"1405.0157","kind":"arxiv","version":1}},"canonical_sha256":"97e45cabe7036a38391ce123ce08782e8408b75181e7232b4a4a3097c42386ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e45cabe7036a38391ce123ce08782e8408b75181e7232b4a4a3097c42386ca","first_computed_at":"2026-05-18T01:43:21.066387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:21.066387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLRxAOMtvwgshispUyI1UVFtu+5gNpEmHc2/A7pga6Uf9L88wGB17A8SeU00+2Hpj5+FMxv+aG5JlecwhmIuDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:21.066887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78884404457c84e8802efc1476773fd9d08853ebbed3c36205d942d29f5916d","sha256:7ed97e66fe3a0902c50c5e132bac269f399cabf3e472f5a9ab9a06190cd2cad5"],"state_sha256":"c833c7825547e1332cd2c6705b20f33dc349c009ed144c1ca7672022baa9ba1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1dggVw2JBORRZpnIVFxWNXY5yINhbOUlfI9Tqh3SrAXUF0cCz3oPFUmha0KdUgArUEgveCYz0Xr6p1h1m3cDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:46:17.442589Z","bundle_sha256":"9993e6dc9127aa38c707d849eeb7f985e3b4bf144238e1cd9980dfdea43656c6"}}