{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OSRL25C6YEBW56YZLAOLQE3TK5","short_pith_number":"pith:OSRL25C6","schema_version":"1.0","canonical_sha256":"74a2bd745ec1036efb19581cb813735762565f4a40ed3b9ce94476aa336dca9b","source":{"kind":"arxiv","id":"1503.00609","version":2},"attestation_state":"computed","paper":{"title":"Community detection in general stochastic block models: fundamental limits and efficient recovery algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.SI","math.IT"],"primary_cat":"math.PR","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2015-03-02T16:50:58Z","abstract_excerpt":"New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the thresholds. This paper investigates whether a general phenomenon takes place for multiple communities, without imposing symmetry.\n  In the general stochastic block model $\\text{SBM}(n,p,Q)$, $n$ vertices are split into $k$ communities of relative size $\\{p_i\\}_{i \\in [k]}$, and vertices in community $i$ and $j$ connect independently with probability $\\{Q_{i,j}\\}_"},"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":"1503.00609","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-02T16:50:58Z","cross_cats_sorted":["cs.IT","cs.SI","math.IT"],"title_canon_sha256":"7408fa186d29f061b9cdf7ec9c8ba3693b1c9016628590332198c76a187220b8","abstract_canon_sha256":"56b6bb53e932319293dd0ef70bb63cf60bca9ed8c0938260fe998af357f1e6e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:35.612026Z","signature_b64":"3dnG+iEbKSqEMAaYTesW7ge7/k5rBSzE1uu0JvcA16qczavI5pKUzTVqTTmnrmz4mfKlc3PW0Y4EYlnSitkWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74a2bd745ec1036efb19581cb813735762565f4a40ed3b9ce94476aa336dca9b","last_reissued_at":"2026-05-18T02:19:35.611615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:35.611615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Community detection in general stochastic block models: fundamental limits and efficient recovery algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.SI","math.IT"],"primary_cat":"math.PR","authors_text":"Colin Sandon, Emmanuel Abbe","submitted_at":"2015-03-02T16:50:58Z","abstract_excerpt":"New phase transition phenomena have recently been discovered for the stochastic block model, for the special case of two non-overlapping symmetric communities. This gives raise in particular to new algorithmic challenges driven by the thresholds. This paper investigates whether a general phenomenon takes place for multiple communities, without imposing symmetry.\n  In the general stochastic block model $\\text{SBM}(n,p,Q)$, $n$ vertices are split into $k$ communities of relative size $\\{p_i\\}_{i \\in [k]}$, and vertices in community $i$ and $j$ connect independently with probability $\\{Q_{i,j}\\}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00609","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.00609","created_at":"2026-05-18T02:19:35.611674+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00609v2","created_at":"2026-05-18T02:19:35.611674+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00609","created_at":"2026-05-18T02:19:35.611674+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSRL25C6YEBW","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSRL25C6YEBW56YZ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSRL25C6","created_at":"2026-05-18T12:29:34.919912+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/OSRL25C6YEBW56YZLAOLQE3TK5","json":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5.json","graph_json":"https://pith.science/api/pith-number/OSRL25C6YEBW56YZLAOLQE3TK5/graph.json","events_json":"https://pith.science/api/pith-number/OSRL25C6YEBW56YZLAOLQE3TK5/events.json","paper":"https://pith.science/paper/OSRL25C6"},"agent_actions":{"view_html":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5","download_json":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5.json","view_paper":"https://pith.science/paper/OSRL25C6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00609&json=true","fetch_graph":"https://pith.science/api/pith-number/OSRL25C6YEBW56YZLAOLQE3TK5/graph.json","fetch_events":"https://pith.science/api/pith-number/OSRL25C6YEBW56YZLAOLQE3TK5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5/action/storage_attestation","attest_author":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5/action/author_attestation","sign_citation":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5/action/citation_signature","submit_replication":"https://pith.science/pith/OSRL25C6YEBW56YZLAOLQE3TK5/action/replication_record"}},"created_at":"2026-05-18T02:19:35.611674+00:00","updated_at":"2026-05-18T02:19:35.611674+00:00"}