{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:U53KUOSUZSFQBZ5JS3ZRZAWV5P","short_pith_number":"pith:U53KUOSU","canonical_record":{"source":{"id":"1903.05425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-13T11:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"9a8453fbafa3b98ab001c1496e5c9c0534b71c67f6659ceb21e4954b31f49550","abstract_canon_sha256":"05cbfbf325b530740c41b3d0944c0cebdafe973d3531706aa067c8f1a6dc3ee2"},"schema_version":"1.0"},"canonical_sha256":"a776aa3a54cc8b00e7a996f31c82d5ebe468b48b5ca1b2a76359f23f81dab8a8","source":{"kind":"arxiv","id":"1903.05425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05425","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05425v1","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05425","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"U53KUOSUZSFQ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U53KUOSUZSFQBZ5J","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U53KUOSU","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:U53KUOSUZSFQBZ5JS3ZRZAWV5P","target":"record","payload":{"canonical_record":{"source":{"id":"1903.05425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-13T11:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"9a8453fbafa3b98ab001c1496e5c9c0534b71c67f6659ceb21e4954b31f49550","abstract_canon_sha256":"05cbfbf325b530740c41b3d0944c0cebdafe973d3531706aa067c8f1a6dc3ee2"},"schema_version":"1.0"},"canonical_sha256":"a776aa3a54cc8b00e7a996f31c82d5ebe468b48b5ca1b2a76359f23f81dab8a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:24.304488Z","signature_b64":"So6uXIP8vCPH1cY3S9NIaSHoju9jM24yXpVkr2haLlwKmlxpfBHrnHjj0ZN1hWT3XQV6EYyyLeLUZOzSNbnqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a776aa3a54cc8b00e7a996f31c82d5ebe468b48b5ca1b2a76359f23f81dab8a8","last_reissued_at":"2026-05-17T23:51:24.303864Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:24.303864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.05425","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":"2026-05-17T23:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97jqqkcAeINgh3jDWHm/JFnc9s+qy9RGzm7ys25FVbCw0V6E3Co7BY4xPFhRWsSIY5Hvb0otJjIqG9Fc8S+mCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:46.577599Z"},"content_sha256":"c1ed462cb0d57914850ed3b7bad1a6cd096c94bed1b664a9be05ce14185bac59","schema_version":"1.0","event_id":"sha256:c1ed462cb0d57914850ed3b7bad1a6cd096c94bed1b664a9be05ce14185bac59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:U53KUOSUZSFQBZ5JS3ZRZAWV5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2-CLUB is NP-hard for distance to 2-club cluster graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mithilesh Kumar","submitted_at":"2019-03-13T11:42:05Z","abstract_excerpt":"We show that 2-CLUB is NP-hard for distance to 2-club cluster graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05425","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":"2026-05-17T23:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DYC+fi0TEeodobMPCaot2pGV8ebNdWhjvlyBrGc3B+L0uubBMBznYAzC/gMGEdexDotyuFf5lNx+aQ7WDDvXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:46.577937Z"},"content_sha256":"583f9db54989d033771ba8ff5c3453b17a9382711e78206cad0581d0b3d1b1d4","schema_version":"1.0","event_id":"sha256:583f9db54989d033771ba8ff5c3453b17a9382711e78206cad0581d0b3d1b1d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/bundle.json","state_url":"https://pith.science/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/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":"2026-06-08T09:56:46Z","links":{"resolver":"https://pith.science/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P","bundle":"https://pith.science/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/bundle.json","state":"https://pith.science/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U53KUOSUZSFQBZ5JS3ZRZAWV5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U53KUOSUZSFQBZ5JS3ZRZAWV5P","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":"05cbfbf325b530740c41b3d0944c0cebdafe973d3531706aa067c8f1a6dc3ee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-13T11:42:05Z","title_canon_sha256":"9a8453fbafa3b98ab001c1496e5c9c0534b71c67f6659ceb21e4954b31f49550"},"schema_version":"1.0","source":{"id":"1903.05425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05425","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05425v1","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05425","created_at":"2026-05-17T23:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"U53KUOSUZSFQ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U53KUOSUZSFQBZ5J","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U53KUOSU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:583f9db54989d033771ba8ff5c3453b17a9382711e78206cad0581d0b3d1b1d4","target":"graph","created_at":"2026-05-17T23:51:24Z","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 show that 2-CLUB is NP-hard for distance to 2-club cluster graphs.","authors_text":"Mithilesh Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-13T11:42:05Z","title":"2-CLUB is NP-hard for distance to 2-club cluster graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05425","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:c1ed462cb0d57914850ed3b7bad1a6cd096c94bed1b664a9be05ce14185bac59","target":"record","created_at":"2026-05-17T23:51:24Z","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":"05cbfbf325b530740c41b3d0944c0cebdafe973d3531706aa067c8f1a6dc3ee2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-13T11:42:05Z","title_canon_sha256":"9a8453fbafa3b98ab001c1496e5c9c0534b71c67f6659ceb21e4954b31f49550"},"schema_version":"1.0","source":{"id":"1903.05425","kind":"arxiv","version":1}},"canonical_sha256":"a776aa3a54cc8b00e7a996f31c82d5ebe468b48b5ca1b2a76359f23f81dab8a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a776aa3a54cc8b00e7a996f31c82d5ebe468b48b5ca1b2a76359f23f81dab8a8","first_computed_at":"2026-05-17T23:51:24.303864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:24.303864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"So6uXIP8vCPH1cY3S9NIaSHoju9jM24yXpVkr2haLlwKmlxpfBHrnHjj0ZN1hWT3XQV6EYyyLeLUZOzSNbnqBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:24.304488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1ed462cb0d57914850ed3b7bad1a6cd096c94bed1b664a9be05ce14185bac59","sha256:583f9db54989d033771ba8ff5c3453b17a9382711e78206cad0581d0b3d1b1d4"],"state_sha256":"84f665e260d2711140980e5ba34d9d781d6e4eb597de5aa375ae06aea3799139"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2EbfiZGeIlSga+XgqChNDAZbKSkozovWRbpu/4lZUpZJDbn73u2ZPqM7g1vOoZqLxhfnyqE0rhAZUTjsNozCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:56:46.580163Z","bundle_sha256":"19ed425b8e66cf74643fbc3c82fb0405097ba4a5cd881a07856109199a8c78f5"}}