{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NRAPWWNHIPC3F62SLP2FHLSGGT","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":"84852faba021c4a9cbca1899546da1ca0cf45080b38aa07e4742b452c21bf6f7","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-06-22T17:57:27Z","title_canon_sha256":"0359433c995267fb64192d2419fa83d3d3bd179b851cf74b2d1c645dd29a63b0"},"schema_version":"1.0","source":{"id":"1906.09479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.09479","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1906.09479v1","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09479","created_at":"2026-05-17T23:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"NRAPWWNHIPC3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NRAPWWNHIPC3F62S","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NRAPWWNH","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:283da0e4ee09d32d34afb8bb61452050b3fee11aaf189e7d0bb1c12e082c1d73","target":"graph","created_at":"2026-05-17T23:42:37Z","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 tree reconstruction problem is to collect and analyze massive data at the $n$th level of the tree, to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. Its connection to the clustering problem in the setting of the stochastic block model, which has wide applications in machine learning and data mining, has been well established. For the stochastic block model, an \"information-theoretically-solvable-but-computationally-hard\" region, or say \"hybrid-hard phase\", appears whenever the reconstruction bound is not tight of the corresponding reconstruction o","authors_text":"Ning Ning, Wenjian Liu","cross_cats":["cs.LG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-06-22T17:57:27Z","title":"The non-tightness of the reconstruction threshold of a 4 states symmetric model with different in-block and out-block mutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09479","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:c8ab6a98e7b7f3abb2ab13248b0dd859fc3e2a87b3184a0afe345493faa9c80e","target":"record","created_at":"2026-05-17T23:42:37Z","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":"84852faba021c4a9cbca1899546da1ca0cf45080b38aa07e4742b452c21bf6f7","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-06-22T17:57:27Z","title_canon_sha256":"0359433c995267fb64192d2419fa83d3d3bd179b851cf74b2d1c645dd29a63b0"},"schema_version":"1.0","source":{"id":"1906.09479","kind":"arxiv","version":1}},"canonical_sha256":"6c40fb59a743c5b2fb525bf453ae4634e2b1980d34f6df16dc143e5d3f51e01d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c40fb59a743c5b2fb525bf453ae4634e2b1980d34f6df16dc143e5d3f51e01d","first_computed_at":"2026-05-17T23:42:37.890426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:37.890426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nbURvF2lkqRhq9Hyc2e27JZHO9qOyd32GyWndutlP78PRge9yg5Xn0zy1W/nSJ8irwpjHENr0WbLP9LZtU47AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:37.891149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.09479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8ab6a98e7b7f3abb2ab13248b0dd859fc3e2a87b3184a0afe345493faa9c80e","sha256:283da0e4ee09d32d34afb8bb61452050b3fee11aaf189e7d0bb1c12e082c1d73"],"state_sha256":"ce8115c25c983d1447ad4e2a5ef187aa4e4efb34379f22d26a7719a901879e85"}