{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UOPXX4EUOK36HWTNKX2VNNVNE4","short_pith_number":"pith:UOPXX4EU","canonical_record":{"source":{"id":"1604.03778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-13T14:02:45Z","cross_cats_sorted":[],"title_canon_sha256":"fcd3a9fcb4df99e3dbb868eebeabb8f8dd4769b9617c6bd81ad3de7e9f3c058d","abstract_canon_sha256":"f2a94572a932ce176a64e1d35eb8da49d27582c641fd15f624896180cdb34a2f"},"schema_version":"1.0"},"canonical_sha256":"a39f7bf09472b7e3da6d55f556b6ad2707dd5f0f45d5c8d7b3ddc43103d90b2d","source":{"kind":"arxiv","id":"1604.03778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03778","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03778v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03778","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"UOPXX4EUOK36","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UOPXX4EUOK36HWTN","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UOPXX4EU","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UOPXX4EUOK36HWTNKX2VNNVNE4","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-13T14:02:45Z","cross_cats_sorted":[],"title_canon_sha256":"fcd3a9fcb4df99e3dbb868eebeabb8f8dd4769b9617c6bd81ad3de7e9f3c058d","abstract_canon_sha256":"f2a94572a932ce176a64e1d35eb8da49d27582c641fd15f624896180cdb34a2f"},"schema_version":"1.0"},"canonical_sha256":"a39f7bf09472b7e3da6d55f556b6ad2707dd5f0f45d5c8d7b3ddc43103d90b2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:11.090599Z","signature_b64":"01u/hFxmyLJ5bmuVNd6EkLXwGBjCEacEZixhTC1RbzLAHCxZJNdIs++s/x5zWsrxHY19L4c1671MSJITmejWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a39f7bf09472b7e3da6d55f556b6ad2707dd5f0f45d5c8d7b3ddc43103d90b2d","last_reissued_at":"2026-05-18T01:17:11.089729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:11.089729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03778","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+Xf3APpuDdiid3DlobyX0mJbaEu0laPFlY3OWcTh6tNgiYKoCUeUIv0nuSr52RZv81kb1BbMq6VZh0LBYjAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:28:23.594137Z"},"content_sha256":"27efaa4c19cf8c73e8b9e7ac951d6ec0c51504f69054314a2fe202e4e5aa9282","schema_version":"1.0","event_id":"sha256:27efaa4c19cf8c73e8b9e7ac951d6ec0c51504f69054314a2fe202e4e5aa9282"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UOPXX4EUOK36HWTNKX2VNNVNE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elementary knot theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Marc Lackenby","submitted_at":"2016-04-13T14:02:45Z","abstract_excerpt":"The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03778","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":"2026-05-18T01:17:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySpUGyY+u7NE5KSTidfy3AvUCDElqq/kOqOihbdGTsD+WMdxiWHr65mz45TirsWrIK+a5N6HJl/+Ntxjx30GAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:28:23.594811Z"},"content_sha256":"77be5d4ae9cb93c182d2c0857eefa10890f7700c75f0a3ac8df3bbd41b89ad91","schema_version":"1.0","event_id":"sha256:77be5d4ae9cb93c182d2c0857eefa10890f7700c75f0a3ac8df3bbd41b89ad91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/bundle.json","state_url":"https://pith.science/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/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":"2026-05-31T20:28:23Z","links":{"resolver":"https://pith.science/pith/UOPXX4EUOK36HWTNKX2VNNVNE4","bundle":"https://pith.science/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/bundle.json","state":"https://pith.science/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOPXX4EUOK36HWTNKX2VNNVNE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UOPXX4EUOK36HWTNKX2VNNVNE4","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":"f2a94572a932ce176a64e1d35eb8da49d27582c641fd15f624896180cdb34a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-13T14:02:45Z","title_canon_sha256":"fcd3a9fcb4df99e3dbb868eebeabb8f8dd4769b9617c6bd81ad3de7e9f3c058d"},"schema_version":"1.0","source":{"id":"1604.03778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03778","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03778v1","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03778","created_at":"2026-05-18T01:17:11Z"},{"alias_kind":"pith_short_12","alias_value":"UOPXX4EUOK36","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UOPXX4EUOK36HWTN","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UOPXX4EU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:77be5d4ae9cb93c182d2c0857eefa10890f7700c75f0a3ac8df3bbd41b89ad91","target":"graph","created_at":"2026-05-18T01:17:11Z","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 aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.","authors_text":"Marc Lackenby","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-13T14:02:45Z","title":"Elementary knot theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03778","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":"sha256:27efaa4c19cf8c73e8b9e7ac951d6ec0c51504f69054314a2fe202e4e5aa9282","target":"record","created_at":"2026-05-18T01:17:11Z","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":"f2a94572a932ce176a64e1d35eb8da49d27582c641fd15f624896180cdb34a2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-13T14:02:45Z","title_canon_sha256":"fcd3a9fcb4df99e3dbb868eebeabb8f8dd4769b9617c6bd81ad3de7e9f3c058d"},"schema_version":"1.0","source":{"id":"1604.03778","kind":"arxiv","version":1}},"canonical_sha256":"a39f7bf09472b7e3da6d55f556b6ad2707dd5f0f45d5c8d7b3ddc43103d90b2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a39f7bf09472b7e3da6d55f556b6ad2707dd5f0f45d5c8d7b3ddc43103d90b2d","first_computed_at":"2026-05-18T01:17:11.089729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:11.089729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"01u/hFxmyLJ5bmuVNd6EkLXwGBjCEacEZixhTC1RbzLAHCxZJNdIs++s/x5zWsrxHY19L4c1671MSJITmejWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:11.090599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27efaa4c19cf8c73e8b9e7ac951d6ec0c51504f69054314a2fe202e4e5aa9282","sha256:77be5d4ae9cb93c182d2c0857eefa10890f7700c75f0a3ac8df3bbd41b89ad91"],"state_sha256":"04411ec166d427d8c741e537f333419a182c8bdce9cc73517281e853a0acf96e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIcm62+cQoMwvcGyfNtr+vCGFKsCWcOfSX3MBqNwFUZoJDBajTISat33Qdja8aV9jAMelvI1uweGp56HKstVBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:28:23.597666Z","bundle_sha256":"c5e421cb78e31ac32f166471ff10095692fd3939ac765c7c9a11a8e4f7b4bcc3"}}