{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FQXLONKP2D5JQ2ZWYMYP7HR4XW","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":"1c25d21c4b8e04ce34505eec9d293862801206c3c7ad1fe5cb55ee70fdedd700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-11T14:04:14Z","title_canon_sha256":"283592e3fa93cb053dd2af3c11b7feaeadeaa8e468c560d94d529047f94d970f"},"schema_version":"1.0","source":{"id":"1107.2034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2034","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2034v1","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2034","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"FQXLONKP2D5J","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FQXLONKP2D5JQ2ZW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FQXLONKP","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:70abffd9642e880299beccb10d43c2c490bc9601cfeee02bb45bf6484bae30e9","target":"graph","created_at":"2026-05-18T04:18:33Z","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 for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for the negatively twisted, positive Whitehead doubles of all knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 10 crossings.","authors_text":"Cheryl Balm, Efstratia Kalfagianni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-11T14:04:14Z","title":"Cosmetic crossings of genus one knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2034","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:db0a9dea3cdf6d505fbef880141f7b10486a153346b116314ff6eb568d144b9a","target":"record","created_at":"2026-05-18T04:18:33Z","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":"1c25d21c4b8e04ce34505eec9d293862801206c3c7ad1fe5cb55ee70fdedd700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-11T14:04:14Z","title_canon_sha256":"283592e3fa93cb053dd2af3c11b7feaeadeaa8e468c560d94d529047f94d970f"},"schema_version":"1.0","source":{"id":"1107.2034","kind":"arxiv","version":1}},"canonical_sha256":"2c2eb7354fd0fa986b36c330ff9e3cbd959485ea6529a960ce8d939765b798f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c2eb7354fd0fa986b36c330ff9e3cbd959485ea6529a960ce8d939765b798f4","first_computed_at":"2026-05-18T04:18:33.601134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:33.601134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GJxvxGjgn32Z1DuNZ1btIuVB4piNfndfK3IkvO1HrNdFA4V5ttMS7XwNpfahesLXaI2xf1amUxeMjvyos6HUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:33.601543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db0a9dea3cdf6d505fbef880141f7b10486a153346b116314ff6eb568d144b9a","sha256:70abffd9642e880299beccb10d43c2c490bc9601cfeee02bb45bf6484bae30e9"],"state_sha256":"885c4e592b3b43451a6c21e20de6623b07225c4cf3d4c1f12fbd5fc9747b93e6"}