{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FQXLONKP2D5JQ2ZWYMYP7HR4XW","short_pith_number":"pith:FQXLONKP","canonical_record":{"source":{"id":"1107.2034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-11T14:04:14Z","cross_cats_sorted":[],"title_canon_sha256":"283592e3fa93cb053dd2af3c11b7feaeadeaa8e468c560d94d529047f94d970f","abstract_canon_sha256":"1c25d21c4b8e04ce34505eec9d293862801206c3c7ad1fe5cb55ee70fdedd700"},"schema_version":"1.0"},"canonical_sha256":"2c2eb7354fd0fa986b36c330ff9e3cbd959485ea6529a960ce8d939765b798f4","source":{"kind":"arxiv","id":"1107.2034","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FQXLONKP2D5JQ2ZWYMYP7HR4XW","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-07-11T14:04:14Z","cross_cats_sorted":[],"title_canon_sha256":"283592e3fa93cb053dd2af3c11b7feaeadeaa8e468c560d94d529047f94d970f","abstract_canon_sha256":"1c25d21c4b8e04ce34505eec9d293862801206c3c7ad1fe5cb55ee70fdedd700"},"schema_version":"1.0"},"canonical_sha256":"2c2eb7354fd0fa986b36c330ff9e3cbd959485ea6529a960ce8d939765b798f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.601543Z","signature_b64":"GJxvxGjgn32Z1DuNZ1btIuVB4piNfndfK3IkvO1HrNdFA4V5ttMS7XwNpfahesLXaI2xf1amUxeMjvyos6HUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c2eb7354fd0fa986b36c330ff9e3cbd959485ea6529a960ce8d939765b798f4","last_reissued_at":"2026-05-18T04:18:33.601134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.601134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2034","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zV0Bdi7ZQn3aQkqyrW8FhFG84u4SpeH/HaIAmkhpeUGBey8+IcYVf7pPLmRLvAzKvrXVwcJ1qt5mPkKXdIDCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:01:34.922693Z"},"content_sha256":"db0a9dea3cdf6d505fbef880141f7b10486a153346b116314ff6eb568d144b9a","schema_version":"1.0","event_id":"sha256:db0a9dea3cdf6d505fbef880141f7b10486a153346b116314ff6eb568d144b9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FQXLONKP2D5JQ2ZWYMYP7HR4XW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmetic crossings of genus one knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Cheryl Balm, Efstratia Kalfagianni","submitted_at":"2011-07-11T14:04:14Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2034","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4dMsFLAPNgACQ0FtxgDlMT90AxgJrdynC+2dvWbJVOpRXu5EP1I5vyCVYSN/Uc35pB/2NRXWvQxNvNK2Gk/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:01:34.923351Z"},"content_sha256":"70abffd9642e880299beccb10d43c2c490bc9601cfeee02bb45bf6484bae30e9","schema_version":"1.0","event_id":"sha256:70abffd9642e880299beccb10d43c2c490bc9601cfeee02bb45bf6484bae30e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/bundle.json","state_url":"https://pith.science/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T23:01:34Z","links":{"resolver":"https://pith.science/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW","bundle":"https://pith.science/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/bundle.json","state":"https://pith.science/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQXLONKP2D5JQ2ZWYMYP7HR4XW/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01I5F9TphfEBEDEQb0HppqaQAemc/v7fxJkqn7D1h3yYuEgMIRIDag4EBAb9NzxULGu/hZFJYb7hyXKnyrtJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:01:34.927485Z","bundle_sha256":"6515dad89326d644073214f61946eeed72f941586c5d3f6f83533f65bfa01b52"}}