{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:35FUYUJYZJXYC6PQTJZXFKRPEO","short_pith_number":"pith:35FUYUJY","schema_version":"1.0","canonical_sha256":"df4b4c5138ca6f8179f09a7372aa2f238724faf474fc0ed84627633fcb3a03b2","source":{"kind":"arxiv","id":"1105.4287","version":1},"attestation_state":"computed","paper":{"title":"Dehn surgery on knots of wrapping number 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ying-Qing Wu","submitted_at":"2011-05-21T20:17:17Z","abstract_excerpt":"Suppose $K$ is a hyperbolic knot in a solid torus $V$ intersecting a meridian disk $D$ twice. We will show that if $K$ is not the Whitehead knot and the frontier of a regular neighborhood of $K \\cup D$ is incompressible in the knot exterior, then $K$ admits at most one exceptional surgery, which must be toroidal. Embedding $V$ in $S^3$ gives infinitely many knots $K_n$ with a slope $r_n$ corresponding to a slope $r$ of $K$ in $V$. If $r$ surgery on $K$ in $V$ is toroidal then either all but at most three $K_n(r_n)$ are toroidal, or they are all reducible or small Seifert fibered with two commo"},"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":"1105.4287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-05-21T20:17:17Z","cross_cats_sorted":[],"title_canon_sha256":"6fbf4b6cc633b829d69d6599895e09dce409c6f3beba9675fe4dba8c5752cba1","abstract_canon_sha256":"85ea024963d51ab9c927423ee18b3d7ac55c3504d316d05481f0a74524ef5aeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:29.474485Z","signature_b64":"SMrwexMBhmYiffg7hxVqurVNWg4+HWyazBudpReDaiVp6ljZ9OIsagmp2TRbKXE3/OVUFXiV7vikJ8lXebYjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df4b4c5138ca6f8179f09a7372aa2f238724faf474fc0ed84627633fcb3a03b2","last_reissued_at":"2026-05-18T04:21:29.474075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:29.474075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dehn surgery on knots of wrapping number 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ying-Qing Wu","submitted_at":"2011-05-21T20:17:17Z","abstract_excerpt":"Suppose $K$ is a hyperbolic knot in a solid torus $V$ intersecting a meridian disk $D$ twice. We will show that if $K$ is not the Whitehead knot and the frontier of a regular neighborhood of $K \\cup D$ is incompressible in the knot exterior, then $K$ admits at most one exceptional surgery, which must be toroidal. Embedding $V$ in $S^3$ gives infinitely many knots $K_n$ with a slope $r_n$ corresponding to a slope $r$ of $K$ in $V$. If $r$ surgery on $K$ in $V$ is toroidal then either all but at most three $K_n(r_n)$ are toroidal, or they are all reducible or small Seifert fibered with two commo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4287","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.4287","created_at":"2026-05-18T04:21:29.474141+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4287v1","created_at":"2026-05-18T04:21:29.474141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4287","created_at":"2026-05-18T04:21:29.474141+00:00"},{"alias_kind":"pith_short_12","alias_value":"35FUYUJYZJXY","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"35FUYUJYZJXYC6PQ","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"35FUYUJY","created_at":"2026-05-18T12:26:18.847500+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/35FUYUJYZJXYC6PQTJZXFKRPEO","json":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO.json","graph_json":"https://pith.science/api/pith-number/35FUYUJYZJXYC6PQTJZXFKRPEO/graph.json","events_json":"https://pith.science/api/pith-number/35FUYUJYZJXYC6PQTJZXFKRPEO/events.json","paper":"https://pith.science/paper/35FUYUJY"},"agent_actions":{"view_html":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO","download_json":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO.json","view_paper":"https://pith.science/paper/35FUYUJY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4287&json=true","fetch_graph":"https://pith.science/api/pith-number/35FUYUJYZJXYC6PQTJZXFKRPEO/graph.json","fetch_events":"https://pith.science/api/pith-number/35FUYUJYZJXYC6PQTJZXFKRPEO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO/action/storage_attestation","attest_author":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO/action/author_attestation","sign_citation":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO/action/citation_signature","submit_replication":"https://pith.science/pith/35FUYUJYZJXYC6PQTJZXFKRPEO/action/replication_record"}},"created_at":"2026-05-18T04:21:29.474141+00:00","updated_at":"2026-05-18T04:21:29.474141+00:00"}