{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MDHYCMDTMC2BTIXH42N72TV2NZ","short_pith_number":"pith:MDHYCMDT","canonical_record":{"source":{"id":"1812.00139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-01T04:08:46Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"ed6893cf646e38b691f5aea2882c9e5d697f9e3bfdc98835e1897f83beb722a4","abstract_canon_sha256":"1c001ee15e9a1e6a9d1e8b5a21da93a2c1c484e6112ef9a814dea58655185505"},"schema_version":"1.0"},"canonical_sha256":"60cf81307360b419a2e7e69bfd4eba6e6dce455efb26f6f77c5a346b85fc10a0","source":{"kind":"arxiv","id":"1812.00139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00139","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00139v1","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00139","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"MDHYCMDTMC2B","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MDHYCMDTMC2BTIXH","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MDHYCMDT","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MDHYCMDTMC2BTIXH42N72TV2NZ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-01T04:08:46Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"ed6893cf646e38b691f5aea2882c9e5d697f9e3bfdc98835e1897f83beb722a4","abstract_canon_sha256":"1c001ee15e9a1e6a9d1e8b5a21da93a2c1c484e6112ef9a814dea58655185505"},"schema_version":"1.0"},"canonical_sha256":"60cf81307360b419a2e7e69bfd4eba6e6dce455efb26f6f77c5a346b85fc10a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:27.141022Z","signature_b64":"14qIxAwDzY5Q8DDo6gP04SAYRcAvAxVfVXEkYvnejDsdc7pq6HSlJbZheELCOSJZi49+BtIFr6TEDkax3wvdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60cf81307360b419a2e7e69bfd4eba6e6dce455efb26f6f77c5a346b85fc10a0","last_reissued_at":"2026-05-17T23:59:27.140497Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:27.140497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00139","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":"2026-05-17T23:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xg+d+EZ7LM1nKsa+ZtHueXk38b1diMdRzDtBKMZQx0l8pfC8/hWQenxEMuIjNuxnQgOimQD0JladcN0T0juiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:30.337294Z"},"content_sha256":"cc2f9424e03ed77994eaf569e559d22799e01659e5bed0703f5935577ea904e5","schema_version":"1.0","event_id":"sha256:cc2f9424e03ed77994eaf569e559d22799e01659e5bed0703f5935577ea904e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MDHYCMDTMC2BTIXH42N72TV2NZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Number of Connected Components in a Graph: Estimation via Counting Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Ashish Khetan, Harshay Shah, Sewoong Oh","submitted_at":"2018-12-01T04:08:46Z","abstract_excerpt":"Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs, little is known about the connection between the observed subgraph and the number of connected component"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00139","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":"2026-05-17T23:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZUgOzbvGwoGLGRF1JsHLdZTkcPE+FvS1PPTGoCID5DgPRlj68pNDt0axpmRb4FHNzZn801AYx4WbKX2vD/1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:30.338092Z"},"content_sha256":"11fcaf1c280a4dd48c19137e26677b3cc0c1659a823f0e1c77e379231fe0e70c","schema_version":"1.0","event_id":"sha256:11fcaf1c280a4dd48c19137e26677b3cc0c1659a823f0e1c77e379231fe0e70c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/bundle.json","state_url":"https://pith.science/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/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":"2026-06-09T19:05:30Z","links":{"resolver":"https://pith.science/pith/MDHYCMDTMC2BTIXH42N72TV2NZ","bundle":"https://pith.science/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/bundle.json","state":"https://pith.science/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDHYCMDTMC2BTIXH42N72TV2NZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MDHYCMDTMC2BTIXH42N72TV2NZ","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":"1c001ee15e9a1e6a9d1e8b5a21da93a2c1c484e6112ef9a814dea58655185505","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-01T04:08:46Z","title_canon_sha256":"ed6893cf646e38b691f5aea2882c9e5d697f9e3bfdc98835e1897f83beb722a4"},"schema_version":"1.0","source":{"id":"1812.00139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00139","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00139v1","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00139","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"MDHYCMDTMC2B","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MDHYCMDTMC2BTIXH","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MDHYCMDT","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:11fcaf1c280a4dd48c19137e26677b3cc0c1659a823f0e1c77e379231fe0e70c","target":"graph","created_at":"2026-05-17T23:59:27Z","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":"Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such a sampled subgraph is of a fundamental interest. In this work, we focus on estimating the number of connected components. It is a challenging problem and, for general graphs, little is known about the connection between the observed subgraph and the number of connected component","authors_text":"Ashish Khetan, Harshay Shah, Sewoong Oh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-01T04:08:46Z","title":"Number of Connected Components in a Graph: Estimation via Counting Patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00139","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:cc2f9424e03ed77994eaf569e559d22799e01659e5bed0703f5935577ea904e5","target":"record","created_at":"2026-05-17T23:59:27Z","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":"1c001ee15e9a1e6a9d1e8b5a21da93a2c1c484e6112ef9a814dea58655185505","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-01T04:08:46Z","title_canon_sha256":"ed6893cf646e38b691f5aea2882c9e5d697f9e3bfdc98835e1897f83beb722a4"},"schema_version":"1.0","source":{"id":"1812.00139","kind":"arxiv","version":1}},"canonical_sha256":"60cf81307360b419a2e7e69bfd4eba6e6dce455efb26f6f77c5a346b85fc10a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60cf81307360b419a2e7e69bfd4eba6e6dce455efb26f6f77c5a346b85fc10a0","first_computed_at":"2026-05-17T23:59:27.140497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.140497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"14qIxAwDzY5Q8DDo6gP04SAYRcAvAxVfVXEkYvnejDsdc7pq6HSlJbZheELCOSJZi49+BtIFr6TEDkax3wvdDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.141022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc2f9424e03ed77994eaf569e559d22799e01659e5bed0703f5935577ea904e5","sha256:11fcaf1c280a4dd48c19137e26677b3cc0c1659a823f0e1c77e379231fe0e70c"],"state_sha256":"9cec6697690f94c0091a8f29bc8271933086785fd6b753c8d76b249336f47841"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EN2ozZlEq5wHXm6xndoZiD2+Nw2TiQ7/lsHK0YCpglBT9oYaZr+DimH/a/8zY+WlPVWsuDT0i5aa/SHZBs0uAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:05:30.342491Z","bundle_sha256":"42bfe55435c41a5220a2cd55269e6e564ae57d79cceb46061b28228cd412898c"}}