{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RXI2QMZ72AJA5RJFAHBWEEO3SX","short_pith_number":"pith:RXI2QMZ7","schema_version":"1.0","canonical_sha256":"8dd1a8333fd0120ec52501c36211db95d3ba76422e939a501d484b04275627d9","source":{"kind":"arxiv","id":"1111.3562","version":2},"attestation_state":"computed","paper":{"title":"Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Donghi Lee, Makoto Sakuma","submitted_at":"2011-11-06T07:48:43Z","abstract_excerpt":"This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the 2-bridge torus links, and the second paper treated the case of 2-bridge links of slope $n/(2n+1)$ and $(n+1)/(3n+2)$, where $n \\ge 2$ is an arbitrary integer. In this paper, we first treat the case of 2-bridge links of slope $n/(mn+1)$ and $(n+1)/((m+1)n+m)$, where $m \\ge 3$ is an arbitrary integer, and then treat the remaining cases b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.3562","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-11-06T07:48:43Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"92da7b5a52bda99e6e7f136678a37ae3c1c0cf1d719be253a758fa62821be875","abstract_canon_sha256":"66816a300e5b02ed6890f8a94eea146a48d8b7be3b36380902ac08bc10e78d7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:47.304830Z","signature_b64":"O1GLlODSDeM3w9ie3zv5zxMxcDu7wfb2KpvzUX+Ifyr0BebOe+LA3/A20nD1Cy0M98RDGCKbwVRtJn/alCbLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dd1a8333fd0120ec52501c36211db95d3ba76422e939a501d484b04275627d9","last_reissued_at":"2026-05-18T03:11:47.304237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:47.304237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopically equivalent simple loops on 2-bridge spheres in 2-bridge link complements (III)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Donghi Lee, Makoto Sakuma","submitted_at":"2011-11-06T07:48:43Z","abstract_excerpt":"This is the last of a series of papers which give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in a 2-bridge link complement to be homotopic in the link complement. The first paper of the series treated the case of the 2-bridge torus links, and the second paper treated the case of 2-bridge links of slope $n/(2n+1)$ and $(n+1)/(3n+2)$, where $n \\ge 2$ is an arbitrary integer. In this paper, we first treat the case of 2-bridge links of slope $n/(mn+1)$ and $(n+1)/((m+1)n+m)$, where $m \\ge 3$ is an arbitrary integer, and then treat the remaining cases b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3562","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.3562","created_at":"2026-05-18T03:11:47.304339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.3562v2","created_at":"2026-05-18T03:11:47.304339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3562","created_at":"2026-05-18T03:11:47.304339+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXI2QMZ72AJA","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXI2QMZ72AJA5RJF","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXI2QMZ7","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX","json":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX.json","graph_json":"https://pith.science/api/pith-number/RXI2QMZ72AJA5RJFAHBWEEO3SX/graph.json","events_json":"https://pith.science/api/pith-number/RXI2QMZ72AJA5RJFAHBWEEO3SX/events.json","paper":"https://pith.science/paper/RXI2QMZ7"},"agent_actions":{"view_html":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX","download_json":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX.json","view_paper":"https://pith.science/paper/RXI2QMZ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.3562&json=true","fetch_graph":"https://pith.science/api/pith-number/RXI2QMZ72AJA5RJFAHBWEEO3SX/graph.json","fetch_events":"https://pith.science/api/pith-number/RXI2QMZ72AJA5RJFAHBWEEO3SX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX/action/storage_attestation","attest_author":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX/action/author_attestation","sign_citation":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX/action/citation_signature","submit_replication":"https://pith.science/pith/RXI2QMZ72AJA5RJFAHBWEEO3SX/action/replication_record"}},"created_at":"2026-05-18T03:11:47.304339+00:00","updated_at":"2026-05-18T03:11:47.304339+00:00"}