{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:CCEYZFLD32FUT3U6O5AEVWT4L5","short_pith_number":"pith:CCEYZFLD","schema_version":"1.0","canonical_sha256":"10898c9563de8b49ee9e77404ada7c5f688071147a78ba068be1300a76e8b32b","source":{"kind":"arxiv","id":"math/0502371","version":2},"attestation_state":"computed","paper":{"title":"Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Kokoro Tanaka","submitted_at":"2005-02-17T09:27:45Z","abstract_excerpt":"Khovanov introduced a cohomology theory for oriented classical links whose graded Euler characteristic is the Jones polynomial. Since Khovanov's theory is functorial for link cobordisms between classical links, we obtain an invariant of a surface-knot, called the {\\it Khovanov-Jacobsson number}, by considering the surface-knot as a link cobordism between empty links. In this paper, we define an invariant of a surface-knot which is a generalization of the Khovanov-Jacobsson number by using Bar-Natan's theory, and prove that any $T^2$-knot has the trivial Khovanov-Jacobsson number."},"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":"math/0502371","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-02-17T09:27:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c2c5cdbe69a14da475be25f4ea4e3f56595d1f9685470954bd9a3b007d951798","abstract_canon_sha256":"0c161e0b7b59af895b6177ca4ffd6a0d8ddc966d91c1fc3f2176e5cf6534b784"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:37.338997Z","signature_b64":"LE4NahkgUB9GW81OcIE8v0U89sd3PqjcPjN3q1atilu4CcOypOgbjw37kwAwqz+aqDcIooWuyKZc5lwBCnbxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10898c9563de8b49ee9e77404ada7c5f688071147a78ba068be1300a76e8b32b","last_reissued_at":"2026-07-04T14:39:37.338608Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:37.338608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan's theory","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Kokoro Tanaka","submitted_at":"2005-02-17T09:27:45Z","abstract_excerpt":"Khovanov introduced a cohomology theory for oriented classical links whose graded Euler characteristic is the Jones polynomial. Since Khovanov's theory is functorial for link cobordisms between classical links, we obtain an invariant of a surface-knot, called the {\\it Khovanov-Jacobsson number}, by considering the surface-knot as a link cobordism between empty links. In this paper, we define an invariant of a surface-knot which is a generalization of the Khovanov-Jacobsson number by using Bar-Natan's theory, and prove that any $T^2$-knot has the trivial Khovanov-Jacobsson number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502371","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0502371/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0502371","created_at":"2026-07-04T14:39:37.338668+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0502371v2","created_at":"2026-07-04T14:39:37.338668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502371","created_at":"2026-07-04T14:39:37.338668+00:00"},{"alias_kind":"pith_short_12","alias_value":"CCEYZFLD32FU","created_at":"2026-07-04T14:39:37.338668+00:00"},{"alias_kind":"pith_short_16","alias_value":"CCEYZFLD32FUT3U6","created_at":"2026-07-04T14:39:37.338668+00:00"},{"alias_kind":"pith_short_8","alias_value":"CCEYZFLD","created_at":"2026-07-04T14:39:37.338668+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/CCEYZFLD32FUT3U6O5AEVWT4L5","json":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5.json","graph_json":"https://pith.science/api/pith-number/CCEYZFLD32FUT3U6O5AEVWT4L5/graph.json","events_json":"https://pith.science/api/pith-number/CCEYZFLD32FUT3U6O5AEVWT4L5/events.json","paper":"https://pith.science/paper/CCEYZFLD"},"agent_actions":{"view_html":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5","download_json":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5.json","view_paper":"https://pith.science/paper/CCEYZFLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0502371&json=true","fetch_graph":"https://pith.science/api/pith-number/CCEYZFLD32FUT3U6O5AEVWT4L5/graph.json","fetch_events":"https://pith.science/api/pith-number/CCEYZFLD32FUT3U6O5AEVWT4L5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5/action/storage_attestation","attest_author":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5/action/author_attestation","sign_citation":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5/action/citation_signature","submit_replication":"https://pith.science/pith/CCEYZFLD32FUT3U6O5AEVWT4L5/action/replication_record"}},"created_at":"2026-07-04T14:39:37.338668+00:00","updated_at":"2026-07-04T14:39:37.338668+00:00"}