{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CSXYNDDQUHHMVYRGGWS7IQZHUZ","short_pith_number":"pith:CSXYNDDQ","schema_version":"1.0","canonical_sha256":"14af868c70a1cecae22635a5f44327a64288e363c27ebd557e6e04250f0c479a","source":{"kind":"arxiv","id":"2606.04917","version":1},"attestation_state":"computed","paper":{"title":"Coactions of cocommutative Hopf algebras on skew polynomial rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Daniel Rogalski, Lucas Buzaglo","submitted_at":"2026-06-03T14:12:47Z","abstract_excerpt":"We classify the cocommutative Hopf algebras which coact inner-faithfully on (one-parameter) skew polynomial rings $A_q(n) = \\Bbbk \\langle x_1,\\dots,x_n \\rangle/(x_j x_i - q x_i x_j \\mid i < j)$ for $n = 2$ and $3$. As a direct corollary, we obtain a classification of group gradings on two- and three-variable skew polynomial rings, recovering a result of Crawford in the two-variable case. Our results are achieved via Manin's universal coacting Hopf algebra construction, often denoted $\\underline{\\operatorname{aut}}(A_q(n))$, by classifying all its cocommutative quotients. We therefore also give"},"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":"2606.04917","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-03T14:12:47Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c869bcebbabf8d7faeb6c063ef9dca09c4a76d4fc12e6609f47dbcaa83a6d06f","abstract_canon_sha256":"9ac3f9d978f13ac919493aa76480e90ceaf9abaaa4c035a35996284769d1844c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:55.396809Z","signature_b64":"v/+2rn62qO8BDqMS8+5oGKzVb09/KxQIsvh1BqVWcMEVsncW0Q8pitMXZ61luhnANMIVX/nJD2e3s+3n6GqfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14af868c70a1cecae22635a5f44327a64288e363c27ebd557e6e04250f0c479a","last_reissued_at":"2026-06-04T01:09:55.396179Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:55.396179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coactions of cocommutative Hopf algebras on skew polynomial rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Daniel Rogalski, Lucas Buzaglo","submitted_at":"2026-06-03T14:12:47Z","abstract_excerpt":"We classify the cocommutative Hopf algebras which coact inner-faithfully on (one-parameter) skew polynomial rings $A_q(n) = \\Bbbk \\langle x_1,\\dots,x_n \\rangle/(x_j x_i - q x_i x_j \\mid i < j)$ for $n = 2$ and $3$. As a direct corollary, we obtain a classification of group gradings on two- and three-variable skew polynomial rings, recovering a result of Crawford in the two-variable case. Our results are achieved via Manin's universal coacting Hopf algebra construction, often denoted $\\underline{\\operatorname{aut}}(A_q(n))$, by classifying all its cocommutative quotients. We therefore also give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04917","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/2606.04917/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":"2606.04917","created_at":"2026-06-04T01:09:55.396293+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04917v1","created_at":"2026-06-04T01:09:55.396293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04917","created_at":"2026-06-04T01:09:55.396293+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSXYNDDQUHHM","created_at":"2026-06-04T01:09:55.396293+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSXYNDDQUHHMVYRG","created_at":"2026-06-04T01:09:55.396293+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSXYNDDQ","created_at":"2026-06-04T01:09:55.396293+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/CSXYNDDQUHHMVYRGGWS7IQZHUZ","json":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ.json","graph_json":"https://pith.science/api/pith-number/CSXYNDDQUHHMVYRGGWS7IQZHUZ/graph.json","events_json":"https://pith.science/api/pith-number/CSXYNDDQUHHMVYRGGWS7IQZHUZ/events.json","paper":"https://pith.science/paper/CSXYNDDQ"},"agent_actions":{"view_html":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ","download_json":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ.json","view_paper":"https://pith.science/paper/CSXYNDDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04917&json=true","fetch_graph":"https://pith.science/api/pith-number/CSXYNDDQUHHMVYRGGWS7IQZHUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CSXYNDDQUHHMVYRGGWS7IQZHUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ/action/storage_attestation","attest_author":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ/action/author_attestation","sign_citation":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ/action/citation_signature","submit_replication":"https://pith.science/pith/CSXYNDDQUHHMVYRGGWS7IQZHUZ/action/replication_record"}},"created_at":"2026-06-04T01:09:55.396293+00:00","updated_at":"2026-06-04T01:09:55.396293+00:00"}