{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3DHJ73WGKFXMEZMEHRV6F2ZLAO","short_pith_number":"pith:3DHJ73WG","schema_version":"1.0","canonical_sha256":"d8ce9feec6516ec265843c6be2eb2b0393ec0301672948943692eb01018231b5","source":{"kind":"arxiv","id":"1511.00546","version":3},"attestation_state":"computed","paper":{"title":"An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SI","stat.ML"],"primary_cat":"math.PR","authors_text":"Laurent Massouli\\'e, Lennart Gulikers, Marc Lelarge","submitted_at":"2015-11-02T15:30:40Z","abstract_excerpt":"We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on $n$ nodes, having i.i.d. weights $(\\phi_u)_{u=1}^n$ (possibly heavy-tailed), partitioned into $q \\geq 2$ asymptotically equal-sized clusters. The model parameters are two constants $a,b > 0$ and the finite second moment of the weights $\\Phi^{(2)}$. Vertices $u$ and $v$ are connected by an edge with probability $\\frac{\\phi_u \\phi_v}{n}a$ when they are in the same class and with probability $\\frac{\\phi_u \\phi_v}{n}b$ otherwise.\n  We prove that it is information-theoretically impossible to estimate the clusters in"},"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":"1511.00546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-02T15:30:40Z","cross_cats_sorted":["cs.LG","cs.SI","stat.ML"],"title_canon_sha256":"e5f56700219efc41ee7b777f021285850abdb4367f464cf864ee6390d7d525d2","abstract_canon_sha256":"bc2e9a64b940ce826c864fa1a91254ef39c921f23e3e02261dd62c05069f38b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:02.836309Z","signature_b64":"u8cNCnpRoNz79DKwuwEWhWvamHfP1saHRgPBMLNGTneZQHd3jiY57KiGZExuzyhYP4k9rrqcHSG1PHzE9kdxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8ce9feec6516ec265843c6be2eb2b0393ec0301672948943692eb01018231b5","last_reissued_at":"2026-05-18T00:00:02.835844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:02.835844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SI","stat.ML"],"primary_cat":"math.PR","authors_text":"Laurent Massouli\\'e, Lennart Gulikers, Marc Lelarge","submitted_at":"2015-11-02T15:30:40Z","abstract_excerpt":"We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on $n$ nodes, having i.i.d. weights $(\\phi_u)_{u=1}^n$ (possibly heavy-tailed), partitioned into $q \\geq 2$ asymptotically equal-sized clusters. The model parameters are two constants $a,b > 0$ and the finite second moment of the weights $\\Phi^{(2)}$. Vertices $u$ and $v$ are connected by an edge with probability $\\frac{\\phi_u \\phi_v}{n}a$ when they are in the same class and with probability $\\frac{\\phi_u \\phi_v}{n}b$ otherwise.\n  We prove that it is information-theoretically impossible to estimate the clusters in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00546","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":"1511.00546","created_at":"2026-05-18T00:00:02.835910+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.00546v3","created_at":"2026-05-18T00:00:02.835910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00546","created_at":"2026-05-18T00:00:02.835910+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DHJ73WGKFXM","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DHJ73WGKFXMEZME","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DHJ73WG","created_at":"2026-05-18T12:29:02.477457+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/3DHJ73WGKFXMEZMEHRV6F2ZLAO","json":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO.json","graph_json":"https://pith.science/api/pith-number/3DHJ73WGKFXMEZMEHRV6F2ZLAO/graph.json","events_json":"https://pith.science/api/pith-number/3DHJ73WGKFXMEZMEHRV6F2ZLAO/events.json","paper":"https://pith.science/paper/3DHJ73WG"},"agent_actions":{"view_html":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO","download_json":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO.json","view_paper":"https://pith.science/paper/3DHJ73WG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.00546&json=true","fetch_graph":"https://pith.science/api/pith-number/3DHJ73WGKFXMEZMEHRV6F2ZLAO/graph.json","fetch_events":"https://pith.science/api/pith-number/3DHJ73WGKFXMEZMEHRV6F2ZLAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO/action/storage_attestation","attest_author":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO/action/author_attestation","sign_citation":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO/action/citation_signature","submit_replication":"https://pith.science/pith/3DHJ73WGKFXMEZMEHRV6F2ZLAO/action/replication_record"}},"created_at":"2026-05-18T00:00:02.835910+00:00","updated_at":"2026-05-18T00:00:02.835910+00:00"}