{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2KLQMVKBZQMNTZ3WVRX3565URH","short_pith_number":"pith:2KLQMVKB","schema_version":"1.0","canonical_sha256":"d297065541cc18d9e776ac6fbefbb489e01cc4f772bb60b05d194c46374e72c3","source":{"kind":"arxiv","id":"1103.1412","version":3},"attestation_state":"computed","paper":{"title":"2-strand twisting and knots with identical quantum knot homologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andrew Lobb","submitted_at":"2011-03-08T01:19:22Z","abstract_excerpt":"Given a knot, we ask how its Khovanov and Khovanov-Rozansky homologies change under the operation of introducing twists in a pair of strands. We obtain long exact sequences in homology and further algebraic structure which is then used to derive topological and computational results. Two of our applications include giving a new way to generate arbitrary numbers of knots with isomorphic homologies and finding an infinite number of mutant knot pairs with isomorphic reduced homologies."},"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":"1103.1412","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-03-08T01:19:22Z","cross_cats_sorted":[],"title_canon_sha256":"eccab8ae664813b838a2d965530052388ed2dc9a384dc1c2781c5abcdd82a348","abstract_canon_sha256":"d6e1d00a3580208bd0e69507cda51ff56225fcc8b66eae6e5a8eb816c9b4483d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:13.383001Z","signature_b64":"aFOmtLyguW9d2gPRABF2tQ3ZvHE6Jm9wmGJb261sHm9QESeivjk+ePfpXDn5vUaEGeaNwi5Duh4pJ0gGB0OMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d297065541cc18d9e776ac6fbefbb489e01cc4f772bb60b05d194c46374e72c3","last_reissued_at":"2026-05-18T02:46:13.382332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:13.382332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-strand twisting and knots with identical quantum knot homologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andrew Lobb","submitted_at":"2011-03-08T01:19:22Z","abstract_excerpt":"Given a knot, we ask how its Khovanov and Khovanov-Rozansky homologies change under the operation of introducing twists in a pair of strands. We obtain long exact sequences in homology and further algebraic structure which is then used to derive topological and computational results. Two of our applications include giving a new way to generate arbitrary numbers of knots with isomorphic homologies and finding an infinite number of mutant knot pairs with isomorphic reduced homologies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1412","kind":"arxiv","version":3},"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":"1103.1412","created_at":"2026-05-18T02:46:13.382462+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1412v3","created_at":"2026-05-18T02:46:13.382462+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1412","created_at":"2026-05-18T02:46:13.382462+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KLQMVKBZQMN","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KLQMVKBZQMNTZ3W","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KLQMVKB","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/2KLQMVKBZQMNTZ3WVRX3565URH","json":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH.json","graph_json":"https://pith.science/api/pith-number/2KLQMVKBZQMNTZ3WVRX3565URH/graph.json","events_json":"https://pith.science/api/pith-number/2KLQMVKBZQMNTZ3WVRX3565URH/events.json","paper":"https://pith.science/paper/2KLQMVKB"},"agent_actions":{"view_html":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH","download_json":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH.json","view_paper":"https://pith.science/paper/2KLQMVKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1412&json=true","fetch_graph":"https://pith.science/api/pith-number/2KLQMVKBZQMNTZ3WVRX3565URH/graph.json","fetch_events":"https://pith.science/api/pith-number/2KLQMVKBZQMNTZ3WVRX3565URH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH/action/storage_attestation","attest_author":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH/action/author_attestation","sign_citation":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH/action/citation_signature","submit_replication":"https://pith.science/pith/2KLQMVKBZQMNTZ3WVRX3565URH/action/replication_record"}},"created_at":"2026-05-18T02:46:13.382462+00:00","updated_at":"2026-05-18T02:46:13.382462+00:00"}