{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3GLLAB4A47W6HPS2DHSAJQOFJU","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":"3571483ff46fded537657d2b031ecf1490d935a7ff0d1c6071775300d07ae71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-10T02:58:12Z","title_canon_sha256":"61f12606d63515df34070ad7d8ff0bc2ad759bf4e8b0bccbe14b6eedd2eb8ad7"},"schema_version":"1.0","source":{"id":"1410.2666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2666","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2666v1","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2666","created_at":"2026-05-18T02:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"3GLLAB4A47W6","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GLLAB4A47W6HPS2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GLLAB4A","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:7eebc5c9987bb341d90efa22b880289b777baf9af9c3a7bc28ea333339847eac","target":"graph","created_at":"2026-05-18T02:40:37Z","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":"The set consisting of all rotations of the Euclidean plane is equipped with a quandle structure. We show that a knot is colorable by this quandle if and only if its Alexander polynomial has a root on the unit circle in $\\mathbb{C}$. Further we enumerate all non-trivial colorings of a torus knot diagram by the quandle using PL trochoids. As an application of these results, we have the complete factorization of the Alexander polynomial of the torus knot.","authors_text":"Ayumu Inoue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-10T02:58:12Z","title":"On colorability of knots by rotations, Torus knot and PL trochoid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2666","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":"sha256:676093d9eecba9bb38e50798d2849fbd8b3704bbccff7d2d63412c380075b7f7","target":"record","created_at":"2026-05-18T02:40:37Z","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":"3571483ff46fded537657d2b031ecf1490d935a7ff0d1c6071775300d07ae71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-10T02:58:12Z","title_canon_sha256":"61f12606d63515df34070ad7d8ff0bc2ad759bf4e8b0bccbe14b6eedd2eb8ad7"},"schema_version":"1.0","source":{"id":"1410.2666","kind":"arxiv","version":1}},"canonical_sha256":"d996b00780e7ede3be5a19e404c1c54d157f984fe03e49062cdd62b3c8be69fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d996b00780e7ede3be5a19e404c1c54d157f984fe03e49062cdd62b3c8be69fa","first_computed_at":"2026-05-18T02:40:37.600462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:37.600462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YkqPgg+kMudkhWEgxe7lUTHbSTPdEWn+hCn619xhfFKBq/hBxX8LzEcoltPpbTcbcD5/ug45goO1PzNh9wFYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:37.601170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:676093d9eecba9bb38e50798d2849fbd8b3704bbccff7d2d63412c380075b7f7","sha256:7eebc5c9987bb341d90efa22b880289b777baf9af9c3a7bc28ea333339847eac"],"state_sha256":"33839077392109cdda7786b439e425a6199022db8065f39873bb09f92d9c7d0a"}