{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WZLMZ7OVGPL4SX3FQNN7FJSKDQ","short_pith_number":"pith:WZLMZ7OV","schema_version":"1.0","canonical_sha256":"b656ccfdd533d7c95f65835bf2a64a1c08fd1212ca50afd753f1d85ac4b31810","source":{"kind":"arxiv","id":"1812.00801","version":1},"attestation_state":"computed","paper":{"title":"Shadow biquandles and local biquandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kanako Oshiro","submitted_at":"2018-11-30T07:52:12Z","abstract_excerpt":"Given a shadow biquandle $(B,X)$ composed of a biquandle $B$ and a strongly connected $B$-set $X$, we have a local biquandle structure on $X$. The (co)homology groups of such shadow biquandles are isomorphic to those of the corresponding local biquandles. Moreover, cocycle invariants, of oriented links and oriented surface-links, using such shadow biquandles coincide with those using the corresponding local biquandles. These results imply that for some cases, the Niebrzydowski's theory in [14, 15, 16] for knot-theoretic ternary quasigroups is the same as shadow biquandle theory. We also show t"},"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":"1812.00801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-11-30T07:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"2a23cf032c46da4f1d6c0a9e3bbc3684017ef2743e0b673ae84c6c46ba9d5e82","abstract_canon_sha256":"dc702b39124cb2b0b90f593e314cb661d96a3821b1a88d37e9cf45ab64d49ce8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:18.970359Z","signature_b64":"auNQChYEIhN3+ZIkeGQ3Q9y7gXcURYp5dcqjktoAj5J/nAHaEA5Tn88xrd/GbYWFKZLpWrEgRAUy4WcRCC0aCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b656ccfdd533d7c95f65835bf2a64a1c08fd1212ca50afd753f1d85ac4b31810","last_reissued_at":"2026-05-17T23:59:18.969969Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:18.969969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shadow biquandles and local biquandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kanako Oshiro","submitted_at":"2018-11-30T07:52:12Z","abstract_excerpt":"Given a shadow biquandle $(B,X)$ composed of a biquandle $B$ and a strongly connected $B$-set $X$, we have a local biquandle structure on $X$. The (co)homology groups of such shadow biquandles are isomorphic to those of the corresponding local biquandles. Moreover, cocycle invariants, of oriented links and oriented surface-links, using such shadow biquandles coincide with those using the corresponding local biquandles. These results imply that for some cases, the Niebrzydowski's theory in [14, 15, 16] for knot-theoretic ternary quasigroups is the same as shadow biquandle theory. We also show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00801","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":"1812.00801","created_at":"2026-05-17T23:59:18.970027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00801v1","created_at":"2026-05-17T23:59:18.970027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00801","created_at":"2026-05-17T23:59:18.970027+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZLMZ7OVGPL4","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZLMZ7OVGPL4SX3F","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZLMZ7OV","created_at":"2026-05-18T12:33:01.666342+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/WZLMZ7OVGPL4SX3FQNN7FJSKDQ","json":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ.json","graph_json":"https://pith.science/api/pith-number/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/graph.json","events_json":"https://pith.science/api/pith-number/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/events.json","paper":"https://pith.science/paper/WZLMZ7OV"},"agent_actions":{"view_html":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ","download_json":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ.json","view_paper":"https://pith.science/paper/WZLMZ7OV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00801&json=true","fetch_graph":"https://pith.science/api/pith-number/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/action/storage_attestation","attest_author":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/action/author_attestation","sign_citation":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/action/citation_signature","submit_replication":"https://pith.science/pith/WZLMZ7OVGPL4SX3FQNN7FJSKDQ/action/replication_record"}},"created_at":"2026-05-17T23:59:18.970027+00:00","updated_at":"2026-05-17T23:59:18.970027+00:00"}