{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OPZODNNM3FXTB3TU65CMCYM4TH","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":"f74e2911d428bb57a02b56f4361e040c1c89df28ff1da482a7bc8912d2a2020c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-06-10T15:47:40Z","title_canon_sha256":"9082423a988d4c7463e194464b4e8bcd2b806eac1393639a4e2af9fa9854268b"},"schema_version":"1.0","source":{"id":"1606.03372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03372","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03372v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03372","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"OPZODNNM3FXT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OPZODNNM3FXTB3TU","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OPZODNNM","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:4eb13059e88ee01841e504d4b775044d35e65c2dca3cb442e58eff1a4ff1d3c0","target":"graph","created_at":"2026-05-18T01:12:37Z","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 two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\\neq 0$ or $V_K'''(1)\\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no more than $11$ crossings except for three $10$-crossing knots and five $11$-crossing knots. We also compute the finite type invariant of order $3$ for two-bridge knots and Whitehead doubles, from which we prove several nonexistence results of purely cosmetic surgery.","authors_text":"Kazuhiro Ichihara, Zhongtao Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-06-10T15:47:40Z","title":"A note on Jones polynomial and cosmetic surgery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03372","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:e25a13b87d35720d151b969f38277f962c08b7f63665d80e6122dfd7ffff0721","target":"record","created_at":"2026-05-18T01:12:37Z","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":"f74e2911d428bb57a02b56f4361e040c1c89df28ff1da482a7bc8912d2a2020c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-06-10T15:47:40Z","title_canon_sha256":"9082423a988d4c7463e194464b4e8bcd2b806eac1393639a4e2af9fa9854268b"},"schema_version":"1.0","source":{"id":"1606.03372","kind":"arxiv","version":1}},"canonical_sha256":"73f2e1b5acd96f30ee74f744c1619c99ca9256ad17d47688b7359c59cf8807a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73f2e1b5acd96f30ee74f744c1619c99ca9256ad17d47688b7359c59cf8807a4","first_computed_at":"2026-05-18T01:12:37.027210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.027210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"50g/+EUECWocN5n7jjf1EO9p3xIbPZmjO1/SwPV3umBKbppdnP1Mqi04ghyNfZnZNxRMXybtZrLCui/VGgAuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.027653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e25a13b87d35720d151b969f38277f962c08b7f63665d80e6122dfd7ffff0721","sha256:4eb13059e88ee01841e504d4b775044d35e65c2dca3cb442e58eff1a4ff1d3c0"],"state_sha256":"05bd288bdeaf8498d0df888ad58f33367e592a5039313ec842c44ae198a3c776"}