{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IPO3NH747O3Q3PTYYZKHAD7T7D","short_pith_number":"pith:IPO3NH74","schema_version":"1.0","canonical_sha256":"43ddb69ffcfbb70dbe78c654700ff3f8cab031c3ca8a5dd61910197b7424cf1f","source":{"kind":"arxiv","id":"1311.4115","version":4},"attestation_state":"computed","paper":{"title":"A Proof Of The Block Model Threshold Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.PR","authors_text":"Allan Sly, Elchanan Mossel, Joe Neeman","submitted_at":"2013-11-17T05:16:47Z","abstract_excerpt":"We study a random graph model named the \"block model\" in statistics and the \"planted partition model\" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of $q$ and a within-class edge probability of $p$.\n  A striking conjecture of Decelle, Krzkala, Moore and Zdeborov\\'a based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, $s=(a-b)/2$ and $p=(a"},"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":"1311.4115","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-11-17T05:16:47Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"7445dc12e11943f8e6658741a9596e4cdcae0fca043afc49c1289543c59ebcc4","abstract_canon_sha256":"258468e72afe296658d39c85e47d1420f6bb2f6345ee2af1064a785e4d8434e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:51.223740Z","signature_b64":"rmiApKRue+Nq1+maWmX3BboGXII5VTW/nnmlOhNTfCbwN3eYIuQHpp85zUouIMbjr1efEMXFDh+tvFhDsfesDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43ddb69ffcfbb70dbe78c654700ff3f8cab031c3ca8a5dd61910197b7424cf1f","last_reissued_at":"2026-05-18T01:34:51.223183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:51.223183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Proof Of The Block Model Threshold Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.PR","authors_text":"Allan Sly, Elchanan Mossel, Joe Neeman","submitted_at":"2013-11-17T05:16:47Z","abstract_excerpt":"We study a random graph model named the \"block model\" in statistics and the \"planted partition model\" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of $q$ and a within-class edge probability of $p$.\n  A striking conjecture of Decelle, Krzkala, Moore and Zdeborov\\'a based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, $s=(a-b)/2$ and $p=(a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4115","kind":"arxiv","version":4},"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":"1311.4115","created_at":"2026-05-18T01:34:51.223264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4115v4","created_at":"2026-05-18T01:34:51.223264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4115","created_at":"2026-05-18T01:34:51.223264+00:00"},{"alias_kind":"pith_short_12","alias_value":"IPO3NH747O3Q","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IPO3NH747O3Q3PTY","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IPO3NH74","created_at":"2026-05-18T12:27:46.883200+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/IPO3NH747O3Q3PTYYZKHAD7T7D","json":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D.json","graph_json":"https://pith.science/api/pith-number/IPO3NH747O3Q3PTYYZKHAD7T7D/graph.json","events_json":"https://pith.science/api/pith-number/IPO3NH747O3Q3PTYYZKHAD7T7D/events.json","paper":"https://pith.science/paper/IPO3NH74"},"agent_actions":{"view_html":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D","download_json":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D.json","view_paper":"https://pith.science/paper/IPO3NH74","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4115&json=true","fetch_graph":"https://pith.science/api/pith-number/IPO3NH747O3Q3PTYYZKHAD7T7D/graph.json","fetch_events":"https://pith.science/api/pith-number/IPO3NH747O3Q3PTYYZKHAD7T7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D/action/storage_attestation","attest_author":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D/action/author_attestation","sign_citation":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D/action/citation_signature","submit_replication":"https://pith.science/pith/IPO3NH747O3Q3PTYYZKHAD7T7D/action/replication_record"}},"created_at":"2026-05-18T01:34:51.223264+00:00","updated_at":"2026-05-18T01:34:51.223264+00:00"}