{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QJ6RYEMQWCHA2K2T56PWCMFAPO","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":"30f1a7722e5c1687129aadcd0a5e563f3d65f4acfbe8e6451fa24102361794fd","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T15:59:01Z","title_canon_sha256":"070bb391ad507dc391a8aff92923d25fef3f18e5e6abce8b56f1c210040a6368"},"schema_version":"1.0","source":{"id":"1309.1380","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1380","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1380v4","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1380","created_at":"2026-05-18T01:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"QJ6RYEMQWCHA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QJ6RYEMQWCHA2K2T","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QJ6RYEMQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:85b6f008ff148de7c721074d3f1f5b0495ebe6897c96303458e0ab184c7d87b8","target":"graph","created_at":"2026-05-18T01:03:53Z","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 problem of reconstructing sparse symmetric block models with two blocks and connection probabilities $a/n$ and $b/n$ for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better than a random guess if and only if $(a-b)^2>2(a+b)$. Using a variant of belief propagation, we give a reconstruction algorithm that is optimal in the sense that if $(a-b)^2>C(a+b)$ for some constant $C$ then our algorithm maximizes the fraction of the nodes labeled correctly. Ours is the only algorithm proven to achieve the optimal fraction of nodes labeled c","authors_text":"Allan Sly, Elchanan Mossel, Joe Neeman","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T15:59:01Z","title":"Belief propagation, robust reconstruction and optimal recovery of block models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1380","kind":"arxiv","version":4},"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:b27a2bbb8206132d77f067ba4ca63a3de8553a3c84558ac3eb765acfc82d343a","target":"record","created_at":"2026-05-18T01:03:53Z","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":"30f1a7722e5c1687129aadcd0a5e563f3d65f4acfbe8e6451fa24102361794fd","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-05T15:59:01Z","title_canon_sha256":"070bb391ad507dc391a8aff92923d25fef3f18e5e6abce8b56f1c210040a6368"},"schema_version":"1.0","source":{"id":"1309.1380","kind":"arxiv","version":4}},"canonical_sha256":"827d1c1190b08e0d2b53ef9f6130a07b861c77d3cc7e0f7a5fda6587bf19846d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"827d1c1190b08e0d2b53ef9f6130a07b861c77d3cc7e0f7a5fda6587bf19846d","first_computed_at":"2026-05-18T01:03:53.713385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:53.713385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2nEnWsl7sHixwRARvleMVWK63LAunHdQMn/cOSM99VcwzNtDvLd+ppvVXb9sLloonnmugP89PJiSfsIza0KFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:53.714036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1380","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b27a2bbb8206132d77f067ba4ca63a3de8553a3c84558ac3eb765acfc82d343a","sha256:85b6f008ff148de7c721074d3f1f5b0495ebe6897c96303458e0ab184c7d87b8"],"state_sha256":"2c8b4b208eb32299bbffc49f940781060e6e0831a65e122056e8998ee1952689"}