{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4L32XYPOFJOBCVOHQI7HRL74E7","short_pith_number":"pith:4L32XYPO","canonical_record":{"source":{"id":"1907.02496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-07-04T17:16:28Z","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"title_canon_sha256":"de64c2124a13980d22accf1e6636bda7d831e7f3db19140bff4c89d3856a02ae","abstract_canon_sha256":"02e651af921b76f3dffb40dafa3182571c140041be673c329c43f2165c6aad92"},"schema_version":"1.0"},"canonical_sha256":"e2f7abe1ee2a5c1155c7823e78affc27fbb2694ce6d3bf8b34148306478517f7","source":{"kind":"arxiv","id":"1907.02496","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02496","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02496v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02496","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"4L32XYPOFJOB","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4L32XYPOFJOBCVOH","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4L32XYPO","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4L32XYPOFJOBCVOHQI7HRL74E7","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-07-04T17:16:28Z","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"title_canon_sha256":"de64c2124a13980d22accf1e6636bda7d831e7f3db19140bff4c89d3856a02ae","abstract_canon_sha256":"02e651af921b76f3dffb40dafa3182571c140041be673c329c43f2165c6aad92"},"schema_version":"1.0"},"canonical_sha256":"e2f7abe1ee2a5c1155c7823e78affc27fbb2694ce6d3bf8b34148306478517f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.428554Z","signature_b64":"1/Nb3XLBAYrCtxpeM5fwTI6Y/ZXCpstIoqQfhcX4yOFKBBV5OwKf7TCkxrUdGiXxx6fgaw4ziJKoGvRrndo0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2f7abe1ee2a5c1155c7823e78affc27fbb2694ce6d3bf8b34148306478517f7","last_reissued_at":"2026-05-17T23:41:28.427901Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.427901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02496","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRDrTJGCmYj4+PtmGUOPrxdfzc4TbsdEESzr5YmCUtejfhliT6VGp8vWaP0E8Ubt3ZRutPSXFwve/iMFXseQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:57:53.503360Z"},"content_sha256":"4a93bc32550a49e2490b542c5b23b16818c1a5d5dfe75295e6997f397df185b6","schema_version":"1.0","event_id":"sha256:4a93bc32550a49e2490b542c5b23b16818c1a5d5dfe75295e6997f397df185b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4L32XYPOFJOBCVOHQI7HRL74E7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Community Detection via the MMSE Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Alexander Volfovsky, Galen Reeves, Vaishakhi Mayya","submitted_at":"2019-07-04T17:16:28Z","abstract_excerpt":"The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. Our results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02496","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtLFXl+WgNOYZ13sap/ZKkWPftS3OGARlJt5Jtmz5zUydcVv+KnJugtdY+xfd2F7sIBBC93WBhWjcMp/kkmYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:57:53.504055Z"},"content_sha256":"eb62404c6a6f29fd363226e8c04c7a399bf72e82b7cbe0b00fa674ce18287f80","schema_version":"1.0","event_id":"sha256:eb62404c6a6f29fd363226e8c04c7a399bf72e82b7cbe0b00fa674ce18287f80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4L32XYPOFJOBCVOHQI7HRL74E7/bundle.json","state_url":"https://pith.science/pith/4L32XYPOFJOBCVOHQI7HRL74E7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4L32XYPOFJOBCVOHQI7HRL74E7/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":"2026-05-27T09:57:53Z","links":{"resolver":"https://pith.science/pith/4L32XYPOFJOBCVOHQI7HRL74E7","bundle":"https://pith.science/pith/4L32XYPOFJOBCVOHQI7HRL74E7/bundle.json","state":"https://pith.science/pith/4L32XYPOFJOBCVOHQI7HRL74E7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4L32XYPOFJOBCVOHQI7HRL74E7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4L32XYPOFJOBCVOHQI7HRL74E7","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":"02e651af921b76f3dffb40dafa3182571c140041be673c329c43f2165c6aad92","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-07-04T17:16:28Z","title_canon_sha256":"de64c2124a13980d22accf1e6636bda7d831e7f3db19140bff4c89d3856a02ae"},"schema_version":"1.0","source":{"id":"1907.02496","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02496","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02496v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02496","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"4L32XYPOFJOB","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4L32XYPOFJOBCVOH","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4L32XYPO","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:eb62404c6a6f29fd363226e8c04c7a399bf72e82b7cbe0b00fa674ce18287f80","target":"graph","created_at":"2026-05-17T23:41:28Z","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 information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow for variability in the sizes and behaviors of the different communities, and thus better reflect the behaviors observed in real-world networks. Our results show that the ability to detect communities can be described succinctly in terms of a matrix of effective signal-to-noise ratios that provides a geometrical representation of the relationships between the d","authors_text":"Alexander Volfovsky, Galen Reeves, Vaishakhi Mayya","cross_cats":["math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-07-04T17:16:28Z","title":"The Geometry of Community Detection via the MMSE Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02496","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":"sha256:4a93bc32550a49e2490b542c5b23b16818c1a5d5dfe75295e6997f397df185b6","target":"record","created_at":"2026-05-17T23:41:28Z","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":"02e651af921b76f3dffb40dafa3182571c140041be673c329c43f2165c6aad92","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-07-04T17:16:28Z","title_canon_sha256":"de64c2124a13980d22accf1e6636bda7d831e7f3db19140bff4c89d3856a02ae"},"schema_version":"1.0","source":{"id":"1907.02496","kind":"arxiv","version":1}},"canonical_sha256":"e2f7abe1ee2a5c1155c7823e78affc27fbb2694ce6d3bf8b34148306478517f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2f7abe1ee2a5c1155c7823e78affc27fbb2694ce6d3bf8b34148306478517f7","first_computed_at":"2026-05-17T23:41:28.427901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:28.427901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/Nb3XLBAYrCtxpeM5fwTI6Y/ZXCpstIoqQfhcX4yOFKBBV5OwKf7TCkxrUdGiXxx6fgaw4ziJKoGvRrndo0Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:28.428554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02496","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a93bc32550a49e2490b542c5b23b16818c1a5d5dfe75295e6997f397df185b6","sha256:eb62404c6a6f29fd363226e8c04c7a399bf72e82b7cbe0b00fa674ce18287f80"],"state_sha256":"527d1b70a1b66f513ce6e49a900558ba0a57b66c4a8c95da5647776274fab4ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y0jrcaiBSrW3B+q7SLCIN8vrd7IwQsY3IKAw0Vd2kKaMqiSIubRk5y3Oh2qU1JCExPaxE1uEdMH+sZCW2BJbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:57:53.507406Z","bundle_sha256":"f860594ce7046105e94caea867f38dafef296b7bc1e00fc1af82180fd9f07484"}}