{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NUAWJMA2KR57ZTZVMSME6PHAPT","short_pith_number":"pith:NUAWJMA2","canonical_record":{"source":{"id":"1507.08685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-30T20:56:38Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"title_canon_sha256":"f69aa6d90243cb458a30c11cc53288b5b5f2a9757b202c2bc2e06901947a1085","abstract_canon_sha256":"bde7a5994fe865398931dee696a14e446f591ee0192b8f448f4d6c94063af6ce"},"schema_version":"1.0"},"canonical_sha256":"6d0164b01a547bfccf3564984f3ce07cc043834360c65e3d61a3f32e0b2160f4","source":{"kind":"arxiv","id":"1507.08685","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08685","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08685v1","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08685","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"NUAWJMA2KR57","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUAWJMA2KR57ZTZV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUAWJMA2","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NUAWJMA2KR57ZTZVMSME6PHAPT","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-30T20:56:38Z","cross_cats_sorted":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"title_canon_sha256":"f69aa6d90243cb458a30c11cc53288b5b5f2a9757b202c2bc2e06901947a1085","abstract_canon_sha256":"bde7a5994fe865398931dee696a14e446f591ee0192b8f448f4d6c94063af6ce"},"schema_version":"1.0"},"canonical_sha256":"6d0164b01a547bfccf3564984f3ce07cc043834360c65e3d61a3f32e0b2160f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:03.151298Z","signature_b64":"Afo+Wmq5z+5Up999K55hSDFqE10vRFTRuqxYq4M4mYMZuBCdkN7q9vJKYA+UnEwbP5Rn4qZDNuBg1AsfmEjJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d0164b01a547bfccf3564984f3ce07cc043834360c65e3d61a3f32e0b2160f4","last_reissued_at":"2026-05-18T01:36:03.150813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:03.150813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08685","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ftRKuTFNwriFK+qL8MMR6hsmSUItpuY3XI1HLLOHMeAVYMRfUo+NvYm4tCDOIi0xq3bg+BCeDFyNhCqKIWVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:52:09.245628Z"},"content_sha256":"212b476542c3e9df9c432520e56258abf1261ff8da093d853cd4d633fed07873","schema_version":"1.0","event_id":"sha256:212b476542c3e9df9c432520e56258abf1261ff8da093d853cd4d633fed07873"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NUAWJMA2KR57ZTZVMSME6PHAPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Mutual Information for the Two-Groups Stochastic Block Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Emmanuel Abbe, Yash Deshpande","submitted_at":"2015-07-30T20:56:38Z","abstract_excerpt":"We develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph $G$ from such a model is generated by first assigning vertex labels at random from a finite alphabet, and then connecting vertices with edge probabilities depending on the labels of the endpoints. In the case of the symmetric two-group model, we establish an explicit `single-letter' characterization of the per-vertex mutual information between the vertex labels and the graph.\n  The explicit expression of the mutual information is intimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08685","kind":"arxiv","version":1},"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":"2026-05-18T01:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWFG76aToYNIegkvkBIj2wb6jeKSSb/3gVbusuX+j/KafRXyMkb2MA8+ZWpC/ak7OtbQ+FDJBG4pk5a8PlelBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:52:09.245977Z"},"content_sha256":"39a2b7842249fb6da66a547943049897c316c2ef21ff0b04d082b32682e7cbc8","schema_version":"1.0","event_id":"sha256:39a2b7842249fb6da66a547943049897c316c2ef21ff0b04d082b32682e7cbc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/bundle.json","state_url":"https://pith.science/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/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":"2026-06-12T10:52:09Z","links":{"resolver":"https://pith.science/pith/NUAWJMA2KR57ZTZVMSME6PHAPT","bundle":"https://pith.science/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/bundle.json","state":"https://pith.science/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUAWJMA2KR57ZTZVMSME6PHAPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NUAWJMA2KR57ZTZVMSME6PHAPT","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":"bde7a5994fe865398931dee696a14e446f591ee0192b8f448f4d6c94063af6ce","cross_cats_sorted":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-30T20:56:38Z","title_canon_sha256":"f69aa6d90243cb458a30c11cc53288b5b5f2a9757b202c2bc2e06901947a1085"},"schema_version":"1.0","source":{"id":"1507.08685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08685","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08685v1","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08685","created_at":"2026-05-18T01:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"NUAWJMA2KR57","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUAWJMA2KR57ZTZV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUAWJMA2","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:39a2b7842249fb6da66a547943049897c316c2ef21ff0b04d082b32682e7cbc8","target":"graph","created_at":"2026-05-18T01:36:03Z","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 develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph $G$ from such a model is generated by first assigning vertex labels at random from a finite alphabet, and then connecting vertices with edge probabilities depending on the labels of the endpoints. In the case of the symmetric two-group model, we establish an explicit `single-letter' characterization of the per-vertex mutual information between the vertex labels and the graph.\n  The explicit expression of the mutual information is intimat","authors_text":"Andrea Montanari, Emmanuel Abbe, Yash Deshpande","cross_cats":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-30T20:56:38Z","title":"Asymptotic Mutual Information for the Two-Groups Stochastic Block Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08685","kind":"arxiv","version":1},"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":"sha256:212b476542c3e9df9c432520e56258abf1261ff8da093d853cd4d633fed07873","target":"record","created_at":"2026-05-18T01:36:03Z","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":"bde7a5994fe865398931dee696a14e446f591ee0192b8f448f4d6c94063af6ce","cross_cats_sorted":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-30T20:56:38Z","title_canon_sha256":"f69aa6d90243cb458a30c11cc53288b5b5f2a9757b202c2bc2e06901947a1085"},"schema_version":"1.0","source":{"id":"1507.08685","kind":"arxiv","version":1}},"canonical_sha256":"6d0164b01a547bfccf3564984f3ce07cc043834360c65e3d61a3f32e0b2160f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d0164b01a547bfccf3564984f3ce07cc043834360c65e3d61a3f32e0b2160f4","first_computed_at":"2026-05-18T01:36:03.150813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:03.150813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Afo+Wmq5z+5Up999K55hSDFqE10vRFTRuqxYq4M4mYMZuBCdkN7q9vJKYA+UnEwbP5Rn4qZDNuBg1AsfmEjJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:03.151298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:212b476542c3e9df9c432520e56258abf1261ff8da093d853cd4d633fed07873","sha256:39a2b7842249fb6da66a547943049897c316c2ef21ff0b04d082b32682e7cbc8"],"state_sha256":"4624f798ed7f7a2fd9f24bd9f66b1e64238659690db07b956680a72d7154ed64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOivf3cfR/3sTjUmsH7IrlCST7z/2NZVLaf98fASWZvqPjGpViEv2iPAEUpyZVRBdiZc+/kh5sQAg8t7A0/EDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:52:09.249392Z","bundle_sha256":"e5de2dadc3b47248d9082d5b02018a1ef31423546871ff9e210c130e893d6085"}}