{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QTJ5QEF2NLJRAEBCNPG7PPK426","short_pith_number":"pith:QTJ5QEF2","schema_version":"1.0","canonical_sha256":"84d3d810ba6ad31010226bcdf7bd5cd79f8afb93ecf31398ea004887c32fc00e","source":{"kind":"arxiv","id":"1406.3543","version":1},"attestation_state":"computed","paper":{"title":"On rack colorings for surface-knot diagrams without branch points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kanako Oshiro, Kokoro Tanaka","submitted_at":"2014-06-13T14:13:08Z","abstract_excerpt":"Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate rack colorings for surface-knot diagrams without branch points and prove that rack colorings are invariants of $S^2$-knots. We also prove that rack colorings for $S^2$-knots can be interpreted in terms of quandles, and discuss a relationship with regular-equivalences of surface-knot diagrams."},"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":"1406.3543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-13T14:13:08Z","cross_cats_sorted":[],"title_canon_sha256":"cbbd8a24f01bcbb02316d8171630050201d50334a8aff56cc030a68f67589eef","abstract_canon_sha256":"d0eb7d84890f79fbef677598172feefc23095872c89eed5cabac114c5aeb314c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:46.479495Z","signature_b64":"4XYHUy0sXts2AAyjzIRi6b0IzfIS1zO2D7kcCaSEMqcP+tEyHd6gmJRpkJ2GjhEzYmP5Rk4kdhQJa7TkhtSTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84d3d810ba6ad31010226bcdf7bd5cd79f8afb93ecf31398ea004887c32fc00e","last_reissued_at":"2026-05-18T02:49:46.479112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:46.479112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On rack colorings for surface-knot diagrams without branch points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kanako Oshiro, Kokoro Tanaka","submitted_at":"2014-06-13T14:13:08Z","abstract_excerpt":"Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate rack colorings for surface-knot diagrams without branch points and prove that rack colorings are invariants of $S^2$-knots. We also prove that rack colorings for $S^2$-knots can be interpreted in terms of quandles, and discuss a relationship with regular-equivalences of surface-knot diagrams."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3543","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":"1406.3543","created_at":"2026-05-18T02:49:46.479174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3543v1","created_at":"2026-05-18T02:49:46.479174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3543","created_at":"2026-05-18T02:49:46.479174+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTJ5QEF2NLJR","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTJ5QEF2NLJRAEBC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTJ5QEF2","created_at":"2026-05-18T12:28:46.137349+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/QTJ5QEF2NLJRAEBCNPG7PPK426","json":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426.json","graph_json":"https://pith.science/api/pith-number/QTJ5QEF2NLJRAEBCNPG7PPK426/graph.json","events_json":"https://pith.science/api/pith-number/QTJ5QEF2NLJRAEBCNPG7PPK426/events.json","paper":"https://pith.science/paper/QTJ5QEF2"},"agent_actions":{"view_html":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426","download_json":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426.json","view_paper":"https://pith.science/paper/QTJ5QEF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3543&json=true","fetch_graph":"https://pith.science/api/pith-number/QTJ5QEF2NLJRAEBCNPG7PPK426/graph.json","fetch_events":"https://pith.science/api/pith-number/QTJ5QEF2NLJRAEBCNPG7PPK426/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426/action/storage_attestation","attest_author":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426/action/author_attestation","sign_citation":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426/action/citation_signature","submit_replication":"https://pith.science/pith/QTJ5QEF2NLJRAEBCNPG7PPK426/action/replication_record"}},"created_at":"2026-05-18T02:49:46.479174+00:00","updated_at":"2026-05-18T02:49:46.479174+00:00"}