{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:7WWSEU7KWCVI4KBKHIDAKVCLRJ","short_pith_number":"pith:7WWSEU7K","schema_version":"1.0","canonical_sha256":"fdad2253eab0aa8e282a3a0605544b8a6ae82ebdc066b2c817d98d209d22d482","source":{"kind":"arxiv","id":"2204.02520","version":1},"attestation_state":"computed","paper":{"title":"Bikei Module Invariants of Unoriented Surface-Links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Sam Nelson, Yewon Joung","submitted_at":"2022-04-05T23:51:10Z","abstract_excerpt":"We extend our previous work from arXiv:1903.06863 on biquandle module invariants of oriented surface-links to the case of unoriented surface-links using bikei modules. The resulting infinite family of enhanced invariants proves be effective at distinguishing unoriented and especially non-orientable surface-links; in particular, we show that these invariants are more effective than the bikei homset cardinality invariant alone at distinguishing non-orientable surface-links. Moreover, as another application we note that our previous biquandle modules which do not satisfy the bikei module axioms a"},"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":"2204.02520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-04-05T23:51:10Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5e3a31b5fee8b47f3f76e3ded406c3ae4f75c2d960fc2cb5c192b7774b973170","abstract_canon_sha256":"e478f8c5629fda67efcb39ac6aa63bba62ba364420c68afd27622c2420205143"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:12:09.132257Z","signature_b64":"uMWHvz2tsAPL1F+LLUbhl7dvDRCHKwsSTSigzgeUSpmw4YA2c295EMt46BITkdKPMMTZwlpPW6w3UvfoHq6qBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdad2253eab0aa8e282a3a0605544b8a6ae82ebdc066b2c817d98d209d22d482","last_reissued_at":"2026-07-05T04:12:09.131854Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:12:09.131854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bikei Module Invariants of Unoriented Surface-Links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Sam Nelson, Yewon Joung","submitted_at":"2022-04-05T23:51:10Z","abstract_excerpt":"We extend our previous work from arXiv:1903.06863 on biquandle module invariants of oriented surface-links to the case of unoriented surface-links using bikei modules. The resulting infinite family of enhanced invariants proves be effective at distinguishing unoriented and especially non-orientable surface-links; in particular, we show that these invariants are more effective than the bikei homset cardinality invariant alone at distinguishing non-orientable surface-links. Moreover, as another application we note that our previous biquandle modules which do not satisfy the bikei module axioms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.02520","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.02520/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":"2204.02520","created_at":"2026-07-05T04:12:09.131907+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.02520v1","created_at":"2026-07-05T04:12:09.131907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.02520","created_at":"2026-07-05T04:12:09.131907+00:00"},{"alias_kind":"pith_short_12","alias_value":"7WWSEU7KWCVI","created_at":"2026-07-05T04:12:09.131907+00:00"},{"alias_kind":"pith_short_16","alias_value":"7WWSEU7KWCVI4KBK","created_at":"2026-07-05T04:12:09.131907+00:00"},{"alias_kind":"pith_short_8","alias_value":"7WWSEU7K","created_at":"2026-07-05T04:12:09.131907+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/7WWSEU7KWCVI4KBKHIDAKVCLRJ","json":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ.json","graph_json":"https://pith.science/api/pith-number/7WWSEU7KWCVI4KBKHIDAKVCLRJ/graph.json","events_json":"https://pith.science/api/pith-number/7WWSEU7KWCVI4KBKHIDAKVCLRJ/events.json","paper":"https://pith.science/paper/7WWSEU7K"},"agent_actions":{"view_html":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ","download_json":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ.json","view_paper":"https://pith.science/paper/7WWSEU7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.02520&json=true","fetch_graph":"https://pith.science/api/pith-number/7WWSEU7KWCVI4KBKHIDAKVCLRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/7WWSEU7KWCVI4KBKHIDAKVCLRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ/action/storage_attestation","attest_author":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ/action/author_attestation","sign_citation":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ/action/citation_signature","submit_replication":"https://pith.science/pith/7WWSEU7KWCVI4KBKHIDAKVCLRJ/action/replication_record"}},"created_at":"2026-07-05T04:12:09.131907+00:00","updated_at":"2026-07-05T04:12:09.131907+00:00"}