{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7EV665ONXXVYML3NTJAETB3P4U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"78a51bd342a200eef87726d270936ee8a970bab34520bd0b98a3370768992313","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-31T17:05:55Z","title_canon_sha256":"1f5b679143cec41352d89412e13765863f967e146b003d0608e0426fd9f90004"},"schema_version":"1.0","source":{"id":"1001.0157","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0157","created_at":"2026-05-18T04:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0157v3","created_at":"2026-05-18T04:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0157","created_at":"2026-05-18T04:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"7EV665ONXXVY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7EV665ONXXVYML3N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7EV665ON","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f9e15c20bbe31b431178d1134a909f68612d1d88245b8e5d0c100e5e5e1e105d","target":"graph","created_at":"2026-05-18T04:06:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We show that every central simple algebra A over a field k is Brauer equivalent to a quotient of a finite dimensional Hopf algebra over the same field (that is- A is Hopf Schur). If the characteristic of the field is zero, or if the algebra has a Galois splitting field of degree prime to the characteristic of k, we can take this Hopf algebra to be semisimple. We also show that if F is any finite extension of k, then F is a quotient of a finite dimensional Hopf algebra over k. We use it in order to show why the algebric closeness assumption is necessary in a weak form of Kaplansky's tenth conje","authors_text":"Ehud Meir","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-31T17:05:55Z","title":"Every central simple algebra is Hopf Schur"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0157","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ef423bee4c8d67f9e3c50d4dd358149dbe7577d85f5f01aeb213c2d253d76da9","target":"record","created_at":"2026-05-18T04:06:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"78a51bd342a200eef87726d270936ee8a970bab34520bd0b98a3370768992313","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-31T17:05:55Z","title_canon_sha256":"1f5b679143cec41352d89412e13765863f967e146b003d0608e0426fd9f90004"},"schema_version":"1.0","source":{"id":"1001.0157","kind":"arxiv","version":3}},"canonical_sha256":"f92bef75cdbdeb862f6d9a4049876fe50f8e352ed5ff7247f21f4d1aca3d01ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f92bef75cdbdeb862f6d9a4049876fe50f8e352ed5ff7247f21f4d1aca3d01ef","first_computed_at":"2026-05-18T04:06:17.845098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:17.845098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n9YQtkyxYIJfNM8TGulTBz2l4Ebu8SWtNwPlK78aTNcIStPFDwkue8FNFXiWN+6CMtBIFkWQ5sLE2HNDOKTlCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:17.846108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0157","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef423bee4c8d67f9e3c50d4dd358149dbe7577d85f5f01aeb213c2d253d76da9","sha256:f9e15c20bbe31b431178d1134a909f68612d1d88245b8e5d0c100e5e5e1e105d"],"state_sha256":"b22bc4ee3c6cf51e9ebc0fe85e7f3b2c9d42d1b01bec455570750d507bded53f"}