{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JVVXOFWKYZHOOHLM4EJO2T6VGA","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":"d9d338be6f05fa738a04e72d70d4dd4ac0ae0be02c3011b619e4a92c89fb0670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-05T08:11:32Z","title_canon_sha256":"04ecacdb597d647db66d34c53d603c30cb94802f59608fa6b1db622f9fe13116"},"schema_version":"1.0","source":{"id":"1502.01450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01450","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01450v1","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01450","created_at":"2026-05-18T02:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"JVVXOFWKYZHO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JVVXOFWKYZHOOHLM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JVVXOFWK","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:b692e6589de0cc51d80e9ca2cde492cb6b1afd4ab2d5bb41cea619832e203b5c","target":"graph","created_at":"2026-05-18T02:27:52Z","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":"By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken surface diagrams. A marked graph diagram is a link diagram possibly with $4$-valent vertices equipped with markers. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of describing surface-links by using marked graph diagrams. In this paper, we give interpretations of these","authors_text":"Jieon Kim, Sang Youl Lee, Seiichi Kamada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-05T08:11:32Z","title":"Computations of quandle cocyle invariants of surface-links using marked graph diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01450","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":"sha256:0fc196e45a75ea23adba90e0c706033cbb78fac8069d8967be51be06abbcc48d","target":"record","created_at":"2026-05-18T02:27:52Z","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":"d9d338be6f05fa738a04e72d70d4dd4ac0ae0be02c3011b619e4a92c89fb0670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-05T08:11:32Z","title_canon_sha256":"04ecacdb597d647db66d34c53d603c30cb94802f59608fa6b1db622f9fe13116"},"schema_version":"1.0","source":{"id":"1502.01450","kind":"arxiv","version":1}},"canonical_sha256":"4d6b7716cac64ee71d6ce112ed4fd5301d01f68b4fe1f0643b1a6054fb9b478e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d6b7716cac64ee71d6ce112ed4fd5301d01f68b4fe1f0643b1a6054fb9b478e","first_computed_at":"2026-05-18T02:27:52.017071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:52.017071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fpxFq2/4AOHVv8MWquJff2fd1u9gbyg8VyabdyTBhOoOrMNUhAPHDipgv+FtfiBG9x3eZQCJQTeFc19XKO6lAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:52.017507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fc196e45a75ea23adba90e0c706033cbb78fac8069d8967be51be06abbcc48d","sha256:b692e6589de0cc51d80e9ca2cde492cb6b1afd4ab2d5bb41cea619832e203b5c"],"state_sha256":"4588f2f2df3ab203ca50f955e4d63090ac711fdcb92ddb46c268376cbbf37050"}