{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QCBB6XWFUNZ4ZKBQCXCNK655DB","short_pith_number":"pith:QCBB6XWF","schema_version":"1.0","canonical_sha256":"80821f5ec5a373cca83015c4d57bbd186fe0090950b289e9dbadae669c4909c8","source":{"kind":"arxiv","id":"1106.3784","version":2},"attestation_state":"computed","paper":{"title":"Mirror-Curves and Knot Mosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ana Zekovic, Ljiljana Radovic, Radmila Sazdanovic, Slavik V. Jablan","submitted_at":"2011-06-19T22:02:20Z","abstract_excerpt":"Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams [3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grids, suitable for software implementation. We provide tables of minimal mirror-curve codes for knots and links "},"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":"1106.3784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-06-19T22:02:20Z","cross_cats_sorted":[],"title_canon_sha256":"8ac516fd1cb54f0aae2e2d0fc3f529370ce3ffef132dfe05e36caa8cb75ed61c","abstract_canon_sha256":"59de49f75b4c0b207bb6ba0bc4240e21e60320cd03cd5ddc06e8af2d495ab9f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:38.603452Z","signature_b64":"m+T2IInSvBxTIl3S5VRgRRw+hnPk0rqXQP7ArXmK9i+Kit9OKwsKisWsZ2IiciUngygrO/i0JFH/iwEo0sS8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80821f5ec5a373cca83015c4d57bbd186fe0090950b289e9dbadae669c4909c8","last_reissued_at":"2026-05-18T04:05:38.602877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:38.602877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mirror-Curves and Knot Mosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ana Zekovic, Ljiljana Radovic, Radmila Sazdanovic, Slavik V. Jablan","submitted_at":"2011-06-19T22:02:20Z","abstract_excerpt":"Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams [3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grids, suitable for software implementation. We provide tables of minimal mirror-curve codes for knots and links "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3784","kind":"arxiv","version":2},"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":"1106.3784","created_at":"2026-05-18T04:05:38.602966+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.3784v2","created_at":"2026-05-18T04:05:38.602966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3784","created_at":"2026-05-18T04:05:38.602966+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCBB6XWFUNZ4","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCBB6XWFUNZ4ZKBQ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCBB6XWF","created_at":"2026-05-18T12:26:39.201973+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/QCBB6XWFUNZ4ZKBQCXCNK655DB","json":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB.json","graph_json":"https://pith.science/api/pith-number/QCBB6XWFUNZ4ZKBQCXCNK655DB/graph.json","events_json":"https://pith.science/api/pith-number/QCBB6XWFUNZ4ZKBQCXCNK655DB/events.json","paper":"https://pith.science/paper/QCBB6XWF"},"agent_actions":{"view_html":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB","download_json":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB.json","view_paper":"https://pith.science/paper/QCBB6XWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.3784&json=true","fetch_graph":"https://pith.science/api/pith-number/QCBB6XWFUNZ4ZKBQCXCNK655DB/graph.json","fetch_events":"https://pith.science/api/pith-number/QCBB6XWFUNZ4ZKBQCXCNK655DB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB/action/storage_attestation","attest_author":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB/action/author_attestation","sign_citation":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB/action/citation_signature","submit_replication":"https://pith.science/pith/QCBB6XWFUNZ4ZKBQCXCNK655DB/action/replication_record"}},"created_at":"2026-05-18T04:05:38.602966+00:00","updated_at":"2026-05-18T04:05:38.602966+00:00"}