{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VEIMFDEKCHC5CCKWXMLHEDODWC","short_pith_number":"pith:VEIMFDEK","schema_version":"1.0","canonical_sha256":"a910c28c8a11c5d10956bb16720dc3b09c259f9fb00dea0433f80f322d647d4b","source":{"kind":"arxiv","id":"1606.00353","version":2},"attestation_state":"computed","paper":{"title":"$f$-Racks, $f$-Quandles, their Extensions and Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.QA"],"primary_cat":"math.RA","authors_text":"A. Makhlouf, Indu R. U. Churchill, M. Elhamdadi, M. Green","submitted_at":"2016-06-01T16:41:31Z","abstract_excerpt":"The purpose of this paper is to introduce and study the notions of $f$-rack and $f$-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order $f$-quandles. Moreover, we define modules over $f$-racks, discuss extensions and define a cohomology complex for $f$-quandles."},"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":"1606.00353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-06-01T16:41:31Z","cross_cats_sorted":["math.AT","math.QA"],"title_canon_sha256":"a77ddaf31539f702f26a9883b7c4c003057949fff7d95b81b7da3e24513b380c","abstract_canon_sha256":"24e48f0cce7d5f04157ff5233e5dc79b465bdf787b99893e7d69ca9be3904a2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:20.407640Z","signature_b64":"Pk8GNsMiB1CyaayxrzDhJUsTiqQAeFdNHy68ljmxYzspzmpWDBh6cuP9aPIPMFICM3rPoqfQZA6JP8La/Nq/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a910c28c8a11c5d10956bb16720dc3b09c259f9fb00dea0433f80f322d647d4b","last_reissued_at":"2026-05-18T00:56:20.406788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:20.406788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$f$-Racks, $f$-Quandles, their Extensions and Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.QA"],"primary_cat":"math.RA","authors_text":"A. Makhlouf, Indu R. U. Churchill, M. Elhamdadi, M. Green","submitted_at":"2016-06-01T16:41:31Z","abstract_excerpt":"The purpose of this paper is to introduce and study the notions of $f$-rack and $f$-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order $f$-quandles. Moreover, we define modules over $f$-racks, discuss extensions and define a cohomology complex for $f$-quandles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00353","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":""},"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":"1606.00353","created_at":"2026-05-18T00:56:20.406915+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00353v2","created_at":"2026-05-18T00:56:20.406915+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00353","created_at":"2026-05-18T00:56:20.406915+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEIMFDEKCHC5","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEIMFDEKCHC5CCKW","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEIMFDEK","created_at":"2026-05-18T12:30:48.956258+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/VEIMFDEKCHC5CCKWXMLHEDODWC","json":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC.json","graph_json":"https://pith.science/api/pith-number/VEIMFDEKCHC5CCKWXMLHEDODWC/graph.json","events_json":"https://pith.science/api/pith-number/VEIMFDEKCHC5CCKWXMLHEDODWC/events.json","paper":"https://pith.science/paper/VEIMFDEK"},"agent_actions":{"view_html":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC","download_json":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC.json","view_paper":"https://pith.science/paper/VEIMFDEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00353&json=true","fetch_graph":"https://pith.science/api/pith-number/VEIMFDEKCHC5CCKWXMLHEDODWC/graph.json","fetch_events":"https://pith.science/api/pith-number/VEIMFDEKCHC5CCKWXMLHEDODWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC/action/storage_attestation","attest_author":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC/action/author_attestation","sign_citation":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC/action/citation_signature","submit_replication":"https://pith.science/pith/VEIMFDEKCHC5CCKWXMLHEDODWC/action/replication_record"}},"created_at":"2026-05-18T00:56:20.406915+00:00","updated_at":"2026-05-18T00:56:20.406915+00:00"}