{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q3THSMETNBZGEQK43DXSNWJKCX","short_pith_number":"pith:Q3THSMET","canonical_record":{"source":{"id":"1801.04339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-12T22:13:48Z","cross_cats_sorted":["cs.DM","cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"e9a8a7e62f4003ed0107a38613740286b987061eb83b1ebdcf16e53ce086ee44","abstract_canon_sha256":"7e90b4e17e263744de05f3bf0faca5715c656a1413554db5e80521a576a5e28b"},"schema_version":"1.0"},"canonical_sha256":"86e6793093687262415cd8ef26d92a15c8cfb2186287a81b432ede479c6bf3d8","source":{"kind":"arxiv","id":"1801.04339","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04339","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04339v3","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04339","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"Q3THSMETNBZG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3THSMETNBZGEQK4","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3THSMET","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q3THSMETNBZGEQK43DXSNWJKCX","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04339","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-12T22:13:48Z","cross_cats_sorted":["cs.DM","cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"e9a8a7e62f4003ed0107a38613740286b987061eb83b1ebdcf16e53ce086ee44","abstract_canon_sha256":"7e90b4e17e263744de05f3bf0faca5715c656a1413554db5e80521a576a5e28b"},"schema_version":"1.0"},"canonical_sha256":"86e6793093687262415cd8ef26d92a15c8cfb2186287a81b432ede479c6bf3d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:18.293628Z","signature_b64":"GtFY4cHxOqThJ8WUZRvDVSr6J81FdXE1HObzpOMk9oao4ZOLPCrtWidu7kH/Omh584sbuwAEI70Mxhlv4YjoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86e6793093687262415cd8ef26d92a15c8cfb2186287a81b432ede479c6bf3d8","last_reissued_at":"2026-05-17T23:43:18.292668Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:18.292668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04339","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvkdNwUf6HwyQJTpe/sC1XLyEOn7jKrRzQpF33DXSCCFp3PmAUT4Ac+OVlAWPC2Xo08VlZ5t0lB+59Gag1knBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:14:35.215109Z"},"content_sha256":"e56dd19c9340702a99b158852bfe5ed96171fd3f2ecff838215c64472040834f","schema_version":"1.0","event_id":"sha256:e56dd19c9340702a99b158852bfe5ed96171fd3f2ecff838215c64472040834f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q3THSMETNBZGEQK43DXSNWJKCX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating the Number of Connected Components in a Graph via Subgraph Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jason M. Klusowski, Yihong Wu","submitted_at":"2018-01-12T22:13:48Z","abstract_excerpt":"Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \\cite{Goodman1949} and Frank \\cite{Frank1978}. We revisit a problem formulated by Frank \\cite{Frank1978} of estimating the number of connected components in a large graph based on the subgraph sampling model, in which we randomly sample a subset of the vertices and observe the induced subgraph. The key question is whether accurate estimation is achievable in the \\emph{sublinear} regime where only a vanishing fraction of the vertices are sampled. We show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04339","kind":"arxiv","version":3},"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":"2026-05-17T23:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wZlmqQHgFrcEt2+mnAQdDN1UAOcGuIb0BJgWysUG3K5YHpK6PfP+P8dHozovDkEfRiw+SNp021msuD1lejHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:14:35.215871Z"},"content_sha256":"81e0530fcb32d4b3dac508ab919fa8230f02d3fdc5b32d6df726dbda6d6f0da3","schema_version":"1.0","event_id":"sha256:81e0530fcb32d4b3dac508ab919fa8230f02d3fdc5b32d6df726dbda6d6f0da3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3THSMETNBZGEQK43DXSNWJKCX/bundle.json","state_url":"https://pith.science/pith/Q3THSMETNBZGEQK43DXSNWJKCX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3THSMETNBZGEQK43DXSNWJKCX/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":"2026-06-08T04:14:35Z","links":{"resolver":"https://pith.science/pith/Q3THSMETNBZGEQK43DXSNWJKCX","bundle":"https://pith.science/pith/Q3THSMETNBZGEQK43DXSNWJKCX/bundle.json","state":"https://pith.science/pith/Q3THSMETNBZGEQK43DXSNWJKCX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3THSMETNBZGEQK43DXSNWJKCX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q3THSMETNBZGEQK43DXSNWJKCX","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":"7e90b4e17e263744de05f3bf0faca5715c656a1413554db5e80521a576a5e28b","cross_cats_sorted":["cs.DM","cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-12T22:13:48Z","title_canon_sha256":"e9a8a7e62f4003ed0107a38613740286b987061eb83b1ebdcf16e53ce086ee44"},"schema_version":"1.0","source":{"id":"1801.04339","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04339","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04339v3","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04339","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"Q3THSMETNBZG","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3THSMETNBZGEQK4","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3THSMET","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:81e0530fcb32d4b3dac508ab919fa8230f02d3fdc5b32d6df726dbda6d6f0da3","target":"graph","created_at":"2026-05-17T23:43:18Z","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":"Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \\cite{Goodman1949} and Frank \\cite{Frank1978}. We revisit a problem formulated by Frank \\cite{Frank1978} of estimating the number of connected components in a large graph based on the subgraph sampling model, in which we randomly sample a subset of the vertices and observe the induced subgraph. The key question is whether accurate estimation is achievable in the \\emph{sublinear} regime where only a vanishing fraction of the vertices are sampled. We show","authors_text":"Jason M. Klusowski, Yihong Wu","cross_cats":["cs.DM","cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-12T22:13:48Z","title":"Estimating the Number of Connected Components in a Graph via Subgraph Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04339","kind":"arxiv","version":3},"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:e56dd19c9340702a99b158852bfe5ed96171fd3f2ecff838215c64472040834f","target":"record","created_at":"2026-05-17T23:43:18Z","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":"7e90b4e17e263744de05f3bf0faca5715c656a1413554db5e80521a576a5e28b","cross_cats_sorted":["cs.DM","cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-12T22:13:48Z","title_canon_sha256":"e9a8a7e62f4003ed0107a38613740286b987061eb83b1ebdcf16e53ce086ee44"},"schema_version":"1.0","source":{"id":"1801.04339","kind":"arxiv","version":3}},"canonical_sha256":"86e6793093687262415cd8ef26d92a15c8cfb2186287a81b432ede479c6bf3d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e6793093687262415cd8ef26d92a15c8cfb2186287a81b432ede479c6bf3d8","first_computed_at":"2026-05-17T23:43:18.292668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.292668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GtFY4cHxOqThJ8WUZRvDVSr6J81FdXE1HObzpOMk9oao4ZOLPCrtWidu7kH/Omh584sbuwAEI70Mxhlv4YjoCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.293628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04339","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e56dd19c9340702a99b158852bfe5ed96171fd3f2ecff838215c64472040834f","sha256:81e0530fcb32d4b3dac508ab919fa8230f02d3fdc5b32d6df726dbda6d6f0da3"],"state_sha256":"4051e799564ae5fd4078631b9b90907cb91ee1ec4a10eed3819c86d6688c3fc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97THPNt+YA4G0ab70e3RJXwA8kQVEdlZ5lfl1a1+v801PtXOCv4eIF/R3JNQP2BCFb6EpC2j5Sz7cWSnYrZeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:14:35.219578Z","bundle_sha256":"80265c3319b01c272454ce43d3161e07cce30bbd85e2723a1a2de75e91b8fc66"}}