{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GMRDBQXKJZFXRDZMRH6G4XJ5WA","short_pith_number":"pith:GMRDBQXK","schema_version":"1.0","canonical_sha256":"332230c2ea4e4b788f2c89fc6e5d3db017417b774a788e75121411e45f4f6ded","source":{"kind":"arxiv","id":"1507.02925","version":3},"attestation_state":"computed","paper":{"title":"Completely random measures for modelling block-structured networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mikkel N. Schmidt, Morten M{\\o}rup, Tue Herlau","submitted_at":"2015-07-10T14:49:52Z","abstract_excerpt":"Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical studies of networks indicate that many real-world networks have a power-law distribution of the vertices which in turn implies the number of edges scale slower than quadratically in the number of vertices. These assumptions are fundamentally irreconcilable as the Aldous-Hoover theorem implies quadratic scaling of the number of edges. Recently Caron and Fox ("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.02925","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-07-10T14:49:52Z","cross_cats_sorted":[],"title_canon_sha256":"1b75a73266a2a6dd4020c1ee99aa3612736df8930d0222d573d523fce644f946","abstract_canon_sha256":"a5714155ad2ce5f40e6dddf4f37e28ba67a880fc2ae57ff5222a810f56069fe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:17.969046Z","signature_b64":"YFcr/HiK2rdX107AYp8rzDXeshUvhLcDJ35yYyhgMu9fNuwbGBvgirTeELx/skxGSW95q/vhmRrBrlkOMjzvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"332230c2ea4e4b788f2c89fc6e5d3db017417b774a788e75121411e45f4f6ded","last_reissued_at":"2026-05-18T01:25:17.968412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:17.968412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Completely random measures for modelling block-structured networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mikkel N. Schmidt, Morten M{\\o}rup, Tue Herlau","submitted_at":"2015-07-10T14:49:52Z","abstract_excerpt":"Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical studies of networks indicate that many real-world networks have a power-law distribution of the vertices which in turn implies the number of edges scale slower than quadratically in the number of vertices. These assumptions are fundamentally irreconcilable as the Aldous-Hoover theorem implies quadratic scaling of the number of edges. Recently Caron and Fox ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02925","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.02925","created_at":"2026-05-18T01:25:17.968527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02925v3","created_at":"2026-05-18T01:25:17.968527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02925","created_at":"2026-05-18T01:25:17.968527+00:00"},{"alias_kind":"pith_short_12","alias_value":"GMRDBQXKJZFX","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GMRDBQXKJZFXRDZM","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GMRDBQXK","created_at":"2026-05-18T12:29:22.688609+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA","json":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA.json","graph_json":"https://pith.science/api/pith-number/GMRDBQXKJZFXRDZMRH6G4XJ5WA/graph.json","events_json":"https://pith.science/api/pith-number/GMRDBQXKJZFXRDZMRH6G4XJ5WA/events.json","paper":"https://pith.science/paper/GMRDBQXK"},"agent_actions":{"view_html":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA","download_json":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA.json","view_paper":"https://pith.science/paper/GMRDBQXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02925&json=true","fetch_graph":"https://pith.science/api/pith-number/GMRDBQXKJZFXRDZMRH6G4XJ5WA/graph.json","fetch_events":"https://pith.science/api/pith-number/GMRDBQXKJZFXRDZMRH6G4XJ5WA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA/action/storage_attestation","attest_author":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA/action/author_attestation","sign_citation":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA/action/citation_signature","submit_replication":"https://pith.science/pith/GMRDBQXKJZFXRDZMRH6G4XJ5WA/action/replication_record"}},"created_at":"2026-05-18T01:25:17.968527+00:00","updated_at":"2026-05-18T01:25:17.968527+00:00"}