{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OP3ZFBK5JCBHYXWUAPACN2AUKU","short_pith_number":"pith:OP3ZFBK5","canonical_record":{"source":{"id":"1404.6325","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-25T05:31:16Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"c61239f32a60766d324c7052e8c0574a0621b99d71d254b056805ed5b5ff6170","abstract_canon_sha256":"56fe74b2659bb67d43e64978361f0009d3d39fc12bcc7866710d9f36d1877ffa"},"schema_version":"1.0"},"canonical_sha256":"73f792855d48827c5ed403c026e8145514e1f443bf629d0c452eab91655e879c","source":{"kind":"arxiv","id":"1404.6325","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6325","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6325v4","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6325","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"OP3ZFBK5JCBH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OP3ZFBK5JCBHYXWU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OP3ZFBK5","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OP3ZFBK5JCBHYXWUAPACN2AUKU","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6325","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-25T05:31:16Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"c61239f32a60766d324c7052e8c0574a0621b99d71d254b056805ed5b5ff6170","abstract_canon_sha256":"56fe74b2659bb67d43e64978361f0009d3d39fc12bcc7866710d9f36d1877ffa"},"schema_version":"1.0"},"canonical_sha256":"73f792855d48827c5ed403c026e8145514e1f443bf629d0c452eab91655e879c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:25.760961Z","signature_b64":"j1m37Ulnx82kdRwjuoPCTnzRVQFKmmtm8EVw5Ub08wMRBt5gy6KAnCehBJGHRZW/4lrjZQjedYez2jroPTVYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73f792855d48827c5ed403c026e8145514e1f443bf629d0c452eab91655e879c","last_reissued_at":"2026-05-18T02:48:25.760364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:25.760364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6325","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hw7MHpoAULFd2Ahvwu007NlAhNyxOWpo3Q/02BbXpIeNdp1rDZj4HnVVBVPizwVOKzLVVMSdy2iUGNzJvmYeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:16:59.360539Z"},"content_sha256":"3ab28083fe2b18a1332896ea3fa4ab78d793bd3217dec79a50ca74440d266c89","schema_version":"1.0","event_id":"sha256:3ab28083fe2b18a1332896ea3fa4ab78d793bd3217dec79a50ca74440d266c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OP3ZFBK5JCBHYXWUAPACN2AUKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global and Local Information in Clustering Labeled Block Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"math.PR","authors_text":"Elchanan Mossel, Tselil Schramm, Varun Kanade","submitted_at":"2014-04-25T05:31:16Z","abstract_excerpt":"The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with intra-cluster edge probability p, and inter-cluster edge probability q. We focus on the sparse case, i.e., p, q = O(1/n), which is practically more relevant and also mathematically more challenging. A conjecture of Decelle, Krzakala, Moore and Zdeborova, based on ideas from statistical physics, predicted a specific threshold for clustering. The negative dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6325","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OXezXUcZ9Zd2eswApDXdMitVVTjP64zh+qrzG3P8D1hEPlZyL02jmNduku5rfpb8Wq8QgWxBGzdtaLgxAZZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:16:59.361171Z"},"content_sha256":"fbcb82c145ffa1bc47e39057c551a62a6a90ff87bece407a95e634f72efc497e","schema_version":"1.0","event_id":"sha256:fbcb82c145ffa1bc47e39057c551a62a6a90ff87bece407a95e634f72efc497e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/bundle.json","state_url":"https://pith.science/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T05:16:59Z","links":{"resolver":"https://pith.science/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU","bundle":"https://pith.science/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/bundle.json","state":"https://pith.science/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OP3ZFBK5JCBHYXWUAPACN2AUKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OP3ZFBK5JCBHYXWUAPACN2AUKU","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":"56fe74b2659bb67d43e64978361f0009d3d39fc12bcc7866710d9f36d1877ffa","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-25T05:31:16Z","title_canon_sha256":"c61239f32a60766d324c7052e8c0574a0621b99d71d254b056805ed5b5ff6170"},"schema_version":"1.0","source":{"id":"1404.6325","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6325","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6325v4","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6325","created_at":"2026-05-18T02:48:25Z"},{"alias_kind":"pith_short_12","alias_value":"OP3ZFBK5JCBH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OP3ZFBK5JCBHYXWU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OP3ZFBK5","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:fbcb82c145ffa1bc47e39057c551a62a6a90ff87bece407a95e634f72efc497e","target":"graph","created_at":"2026-05-18T02:48:25Z","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":"The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with intra-cluster edge probability p, and inter-cluster edge probability q. We focus on the sparse case, i.e., p, q = O(1/n), which is practically more relevant and also mathematically more challenging. A conjecture of Decelle, Krzakala, Moore and Zdeborova, based on ideas from statistical physics, predicted a specific threshold for clustering. The negative dire","authors_text":"Elchanan Mossel, Tselil Schramm, Varun Kanade","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-25T05:31:16Z","title":"Global and Local Information in Clustering Labeled Block Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6325","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":"sha256:3ab28083fe2b18a1332896ea3fa4ab78d793bd3217dec79a50ca74440d266c89","target":"record","created_at":"2026-05-18T02:48:25Z","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":"56fe74b2659bb67d43e64978361f0009d3d39fc12bcc7866710d9f36d1877ffa","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-25T05:31:16Z","title_canon_sha256":"c61239f32a60766d324c7052e8c0574a0621b99d71d254b056805ed5b5ff6170"},"schema_version":"1.0","source":{"id":"1404.6325","kind":"arxiv","version":4}},"canonical_sha256":"73f792855d48827c5ed403c026e8145514e1f443bf629d0c452eab91655e879c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73f792855d48827c5ed403c026e8145514e1f443bf629d0c452eab91655e879c","first_computed_at":"2026-05-18T02:48:25.760364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:25.760364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1m37Ulnx82kdRwjuoPCTnzRVQFKmmtm8EVw5Ub08wMRBt5gy6KAnCehBJGHRZW/4lrjZQjedYez2jroPTVYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:25.760961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6325","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ab28083fe2b18a1332896ea3fa4ab78d793bd3217dec79a50ca74440d266c89","sha256:fbcb82c145ffa1bc47e39057c551a62a6a90ff87bece407a95e634f72efc497e"],"state_sha256":"1c74d7914f58d9477947581899823207766ab4a0a0c0850ec72f4e7224f05e3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TuHhkbteXLvve/4iEYC73cMLOr7z4OdIF8XupZ8SeGWEOJ91MORC9Ey0G6HC4ctpfASpDIumeeQmlkw7bKvKBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:16:59.364689Z","bundle_sha256":"72d674facf53deb036d49c586ddda07d1ce4085f0e1fb35b6ef542e0ae521288"}}