{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2XFO7MUVTE2WSVORQWDE4WYGOW","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":"9a238388493907fe5e7dced735423b88bfd14d64c25aec51e62771d6136f8ce7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-28T06:02:21Z","title_canon_sha256":"798167f216686b332ed5783ad007b5f6b407f16ef5ca1278efb7c3108fb5d61b"},"schema_version":"1.0","source":{"id":"1303.7044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7044","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7044v3","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7044","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"2XFO7MUVTE2W","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2XFO7MUVTE2WSVOR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2XFO7MUV","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:bbc8c4d6aa4fd03d802667fcd756b36f6e7d419dc444e45918d76e0a623808a5","target":"graph","created_at":"2026-05-18T02:38:17Z","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":"Lomonaco and Kauffman introduced a knot mosaic system to give a definition of a quantum knot system which can be viewed as a blueprint for the construction of an actual physical quantum system. A knot $n$-mosaic is an $n \\times n$ matrix of 11 kinds of specific mosaic tiles representing a knot or a link by adjoining properly that is called suitably connected. $D_n$ denotes the total number of all knot $n$-mosaics. Already known is that $D_1=1$, $D_2=2$, and $D_3=22$. In this paper we establish the lower and upper bounds on $D_n$ $$\\frac{2}{275}(9 \\cdot 6^{n-2} + 1)^2 \\cdot 2^{(n-3)^2} \\ \\leq \\","authors_text":"Ho Lee, Hwa Jeong Lee, Kyungpyo Hong, Seungsang Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-28T06:02:21Z","title":"Upper bound on the total number of knot $n$-mosaics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7044","kind":"arxiv","version":3},"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":"sha256:9cbb9fca02924179108d9035fca35dd8b1b26e5c0b5f893b47853a8e9a14df8e","target":"record","created_at":"2026-05-18T02:38:17Z","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":"9a238388493907fe5e7dced735423b88bfd14d64c25aec51e62771d6136f8ce7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-28T06:02:21Z","title_canon_sha256":"798167f216686b332ed5783ad007b5f6b407f16ef5ca1278efb7c3108fb5d61b"},"schema_version":"1.0","source":{"id":"1303.7044","kind":"arxiv","version":3}},"canonical_sha256":"d5caefb29599356955d185864e5b0675b0810609c2811056c159f13f5fa7ced1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5caefb29599356955d185864e5b0675b0810609c2811056c159f13f5fa7ced1","first_computed_at":"2026-05-18T02:38:17.284344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.284344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SWocaJjSu/dwnLoLMJOfIf1ghQCmioLtmCQapmptaD96xXHjMjxm7DFi4cNw1Scbuj7sa/hexFUCmcAxAD3hBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.284991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cbb9fca02924179108d9035fca35dd8b1b26e5c0b5f893b47853a8e9a14df8e","sha256:bbc8c4d6aa4fd03d802667fcd756b36f6e7d419dc444e45918d76e0a623808a5"],"state_sha256":"65bfa57e525b142cf2bae20095a02c8a96a59e7198828491cec4c7a1304c683a"}