{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGXUFU3EA24PEWAIT46KW7CCB3","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":"8aecc82094afe55b9b3ffad365cc7b2ecd7eb4a711f67d1475733d9472ca8d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-04T15:04:31Z","title_canon_sha256":"eae7fad7e1ad4173730a7a3d65c117a972fdbca59c3a277ce551b9075d728abb"},"schema_version":"1.0","source":{"id":"1608.01570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01570","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01570v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01570","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"LGXUFU3EA24P","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGXUFU3EA24PEWAI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGXUFU3E","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:2cdf30477380c24588461c79db9e1eba39c0fca2b5b0d12acb8b3aac2e892ce8","target":"graph","created_at":"2026-05-18T01:09:52Z","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 prove for a large class of knots that the meridional rank coincides with the bridge number. This class contains all knots whose exterior is a graph manifold. This gives a partial answer to a question of S. Cappell and J. Shaneson, see problem 1.11 on Kirby's list.","authors_text":"Ederson Dutra, Michel Boileau, Richard Weidmann, Yeonhee Jang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-04T15:04:31Z","title":"Meridional Rank of Knots Whose Exterior is a Graph Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01570","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":"sha256:3a42bdb6c587cfc7adc8f7c318989d1c54575da25510192056df8f9080d7cf7e","target":"record","created_at":"2026-05-18T01:09:52Z","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":"8aecc82094afe55b9b3ffad365cc7b2ecd7eb4a711f67d1475733d9472ca8d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-08-04T15:04:31Z","title_canon_sha256":"eae7fad7e1ad4173730a7a3d65c117a972fdbca59c3a277ce551b9075d728abb"},"schema_version":"1.0","source":{"id":"1608.01570","kind":"arxiv","version":1}},"canonical_sha256":"59af42d36406b8f258089f3cab7c420edd91dc79130626c635a769ff45d2a1aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59af42d36406b8f258089f3cab7c420edd91dc79130626c635a769ff45d2a1aa","first_computed_at":"2026-05-18T01:09:52.083733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:52.083733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDI4til3xX+nmcmmcD5gR3dz2j/K6ivlzL5nn+UJzx77M4e0tTwfrsB7ws/1jTdoRpjvoF+IanDhViX5C4APBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:52.084365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a42bdb6c587cfc7adc8f7c318989d1c54575da25510192056df8f9080d7cf7e","sha256:2cdf30477380c24588461c79db9e1eba39c0fca2b5b0d12acb8b3aac2e892ce8"],"state_sha256":"4786cb8384ef5ba04cbca4c1b3b479b9a745efed335995b094621917c931d896"}