{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LCHRAG3QMUU7X6Y5NWKBMM3QYG","short_pith_number":"pith:LCHRAG3Q","schema_version":"1.0","canonical_sha256":"588f101b706529fbfb1d6d94163370c185cd8b09c7f05ba8b196b9484f016322","source":{"kind":"arxiv","id":"1602.01558","version":1},"attestation_state":"computed","paper":{"title":"Polynomial of an oriented surface-link diagram via quantum A_2 invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akio Kawauchi, Sang Youl Lee, Seiichi Kamada, Yewon Joung","submitted_at":"2016-02-04T05:06:10Z","abstract_excerpt":"It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduced a regular isotopy invariant, called the quantum A_2 invariant, for tangled trivalent graph diagrams. In this paper, a polynomial for a marked graph diagram is defined by use of the quantum A_2 invariant and it is studied how the polynomial changes under Yoshikawa moves. The notion of a ribbon marked graph is introduced to show that this polynomial is useful for an invariant of a ribbon 2-knot."},"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":"1602.01558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-02-04T05:06:10Z","cross_cats_sorted":[],"title_canon_sha256":"b9e077b9061a172dfd0f1e5fcf8c5f4f11c1c10468713c23a609dc1aebab5399","abstract_canon_sha256":"c1ba9e37de664dc7a3aa03afad5477a19cccd3faa0563cd2018234137fe17200"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:18.648510Z","signature_b64":"NhLVAqNW7XYWe1hi7e9j0TeikNjj77e+rsSTXBNgSiYRLBaGmO76zojKCTt5NIwqqmB6G24U5fLgpoCnuM4sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"588f101b706529fbfb1d6d94163370c185cd8b09c7f05ba8b196b9484f016322","last_reissued_at":"2026-05-18T01:21:18.648062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:18.648062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial of an oriented surface-link diagram via quantum A_2 invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akio Kawauchi, Sang Youl Lee, Seiichi Kamada, Yewon Joung","submitted_at":"2016-02-04T05:06:10Z","abstract_excerpt":"It is known that every surface-link can be presented by a marked graph diagram, and such a diagram presentation is unique up to moves called Yoshikawa moves. G. Kuperberg introduced a regular isotopy invariant, called the quantum A_2 invariant, for tangled trivalent graph diagrams. In this paper, a polynomial for a marked graph diagram is defined by use of the quantum A_2 invariant and it is studied how the polynomial changes under Yoshikawa moves. The notion of a ribbon marked graph is introduced to show that this polynomial is useful for an invariant of a ribbon 2-knot."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01558","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":"1602.01558","created_at":"2026-05-18T01:21:18.648128+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.01558v1","created_at":"2026-05-18T01:21:18.648128+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01558","created_at":"2026-05-18T01:21:18.648128+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCHRAG3QMUU7","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCHRAG3QMUU7X6Y5","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCHRAG3Q","created_at":"2026-05-18T12:30:29.479603+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/LCHRAG3QMUU7X6Y5NWKBMM3QYG","json":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG.json","graph_json":"https://pith.science/api/pith-number/LCHRAG3QMUU7X6Y5NWKBMM3QYG/graph.json","events_json":"https://pith.science/api/pith-number/LCHRAG3QMUU7X6Y5NWKBMM3QYG/events.json","paper":"https://pith.science/paper/LCHRAG3Q"},"agent_actions":{"view_html":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG","download_json":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG.json","view_paper":"https://pith.science/paper/LCHRAG3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.01558&json=true","fetch_graph":"https://pith.science/api/pith-number/LCHRAG3QMUU7X6Y5NWKBMM3QYG/graph.json","fetch_events":"https://pith.science/api/pith-number/LCHRAG3QMUU7X6Y5NWKBMM3QYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG/action/storage_attestation","attest_author":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG/action/author_attestation","sign_citation":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG/action/citation_signature","submit_replication":"https://pith.science/pith/LCHRAG3QMUU7X6Y5NWKBMM3QYG/action/replication_record"}},"created_at":"2026-05-18T01:21:18.648128+00:00","updated_at":"2026-05-18T01:21:18.648128+00:00"}