{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UBQIOHF26NKQ7PHFK4XNHXZJOO","short_pith_number":"pith:UBQIOHF2","schema_version":"1.0","canonical_sha256":"a060871cbaf3550fbce5572ed3df2973b6995d2b2e6db695256c36865a53a767","source":{"kind":"arxiv","id":"2412.16004","version":2},"attestation_state":"computed","paper":{"title":"Presentations for small reflection equation algebras of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.QA","authors_text":"Juliet Cooke, Robert Laugwitz","submitted_at":"2024-12-20T15:54:04Z","abstract_excerpt":"We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\\mathfrak{gl}_n$ and $\\mathfrak{sl}_n$. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types $GL_n$ and $SL_n$ by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately"},"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":"2412.16004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-12-20T15:54:04Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"e75dc80eb8cc6b3d7b274bd0e6f51fbb3efc5a65237adc527cffe055f5b9bae3","abstract_canon_sha256":"b76c82d30676ee321ed634bb8895be83a3f1c1c17ea561869a903ec73a7aae23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:07.587549Z","signature_b64":"2Z/WHysOV6yyS7Pk23S9pm9IDxlXGs8kAkEdI0Yhw6EOxoN8cUuMmD0n4i/n3+KZcqfsxzvFf4UBqvKsFjuyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a060871cbaf3550fbce5572ed3df2973b6995d2b2e6db695256c36865a53a767","last_reissued_at":"2026-07-05T11:20:07.587078Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:07.587078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Presentations for small reflection equation algebras of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.QA","authors_text":"Juliet Cooke, Robert Laugwitz","submitted_at":"2024-12-20T15:54:04Z","abstract_excerpt":"We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\\mathfrak{gl}_n$ and $\\mathfrak{sl}_n$. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types $GL_n$ and $SL_n$ by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16004","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/2412.16004/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":"2412.16004","created_at":"2026-07-05T11:20:07.587134+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.16004v2","created_at":"2026-07-05T11:20:07.587134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16004","created_at":"2026-07-05T11:20:07.587134+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBQIOHF26NKQ","created_at":"2026-07-05T11:20:07.587134+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBQIOHF26NKQ7PHF","created_at":"2026-07-05T11:20:07.587134+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBQIOHF2","created_at":"2026-07-05T11:20:07.587134+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/UBQIOHF26NKQ7PHFK4XNHXZJOO","json":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO.json","graph_json":"https://pith.science/api/pith-number/UBQIOHF26NKQ7PHFK4XNHXZJOO/graph.json","events_json":"https://pith.science/api/pith-number/UBQIOHF26NKQ7PHFK4XNHXZJOO/events.json","paper":"https://pith.science/paper/UBQIOHF2"},"agent_actions":{"view_html":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO","download_json":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO.json","view_paper":"https://pith.science/paper/UBQIOHF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.16004&json=true","fetch_graph":"https://pith.science/api/pith-number/UBQIOHF26NKQ7PHFK4XNHXZJOO/graph.json","fetch_events":"https://pith.science/api/pith-number/UBQIOHF26NKQ7PHFK4XNHXZJOO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO/action/storage_attestation","attest_author":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO/action/author_attestation","sign_citation":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO/action/citation_signature","submit_replication":"https://pith.science/pith/UBQIOHF26NKQ7PHFK4XNHXZJOO/action/replication_record"}},"created_at":"2026-07-05T11:20:07.587134+00:00","updated_at":"2026-07-05T11:20:07.587134+00:00"}