{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JOC6YCJLO3B4VLCORXYO34JPJO","short_pith_number":"pith:JOC6YCJL","schema_version":"1.0","canonical_sha256":"4b85ec092b76c3caac4e8df0edf12f4bbd0b9929ca60624bb23d4ec2c1567d6a","source":{"kind":"arxiv","id":"1609.00517","version":1},"attestation_state":"computed","paper":{"title":"Quantum knot mosaics and the growth constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Seungsang Oh","submitted_at":"2016-09-02T09:26:53Z","abstract_excerpt":"Lomonaco and Kauffman introduced a knot mosaic system to give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot $n$--mosaic is an $n \\times n$ array of 11 mosaic tiles representing a knot or a link diagram by adjoining properly that is called suitably connected. The total number of knot $n$--mosaics is denoted by $D_n$ which is known to grow in a quadratic exponential rate. In this paper, we show the existence of the knot mosaic constant"},"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":"1609.00517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-02T09:26:53Z","cross_cats_sorted":[],"title_canon_sha256":"49917680fd4f88c51beb82b1defe4bbc7b40e5059c04772a828d79b6cd33f197","abstract_canon_sha256":"87a71ce821cf4fd458fdf2a019bf292b55cff1623386835b3dc8a321d1f7ddea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.771450Z","signature_b64":"qaFnvmsXN2SuElO0qRbdvtKaSd6UHJ8Y0l2f3yHrcWqXVdccQ5TSdwTykf94JGSPhKgRnxyubdPC/Bl6ppExCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b85ec092b76c3caac4e8df0edf12f4bbd0b9929ca60624bb23d4ec2c1567d6a","last_reissued_at":"2026-05-18T01:06:23.771094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.771094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum knot mosaics and the growth constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Seungsang Oh","submitted_at":"2016-09-02T09:26:53Z","abstract_excerpt":"Lomonaco and Kauffman introduced a knot mosaic system to give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot $n$--mosaic is an $n \\times n$ array of 11 mosaic tiles representing a knot or a link diagram by adjoining properly that is called suitably connected. The total number of knot $n$--mosaics is denoted by $D_n$ which is known to grow in a quadratic exponential rate. In this paper, we show the existence of the knot mosaic constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00517","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.00517","created_at":"2026-05-18T01:06:23.771151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.00517v1","created_at":"2026-05-18T01:06:23.771151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00517","created_at":"2026-05-18T01:06:23.771151+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOC6YCJLO3B4","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOC6YCJLO3B4VLCO","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOC6YCJL","created_at":"2026-05-18T12:30:25.849896+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/JOC6YCJLO3B4VLCORXYO34JPJO","json":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO.json","graph_json":"https://pith.science/api/pith-number/JOC6YCJLO3B4VLCORXYO34JPJO/graph.json","events_json":"https://pith.science/api/pith-number/JOC6YCJLO3B4VLCORXYO34JPJO/events.json","paper":"https://pith.science/paper/JOC6YCJL"},"agent_actions":{"view_html":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO","download_json":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO.json","view_paper":"https://pith.science/paper/JOC6YCJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.00517&json=true","fetch_graph":"https://pith.science/api/pith-number/JOC6YCJLO3B4VLCORXYO34JPJO/graph.json","fetch_events":"https://pith.science/api/pith-number/JOC6YCJLO3B4VLCORXYO34JPJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO/action/storage_attestation","attest_author":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO/action/author_attestation","sign_citation":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO/action/citation_signature","submit_replication":"https://pith.science/pith/JOC6YCJLO3B4VLCORXYO34JPJO/action/replication_record"}},"created_at":"2026-05-18T01:06:23.771151+00:00","updated_at":"2026-05-18T01:06:23.771151+00:00"}