{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:NYEXDXQY3AU2GWAXO3VIPFVI5M","short_pith_number":"pith:NYEXDXQY","schema_version":"1.0","canonical_sha256":"6e0971de18d829a3581776ea8796a8eb2a1ebcea8da2c12164caca5ba1a3f32c","source":{"kind":"arxiv","id":"1012.4877","version":1},"attestation_state":"computed","paper":{"title":"Essential dimension of simple algebras in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sanghoon Baek","submitted_at":"2010-12-22T04:53:23Z","abstract_excerpt":"Let $p$ be a prime integer, $1\\leq s\\leq r$ integers, $F$ a field of characteristic $p$. Let $\\cat{Dec}_{p^r}$ denote the class of the tensor product of $r$ $p$-symbols and $\\cat{Alg}_{p^r,p^s}$ denote the class of central simple algebras of degree $p^r$ and exponent dividing $p^s$. For any integers $s<r$, we find a lower bound for the essential $p$-dimension of $\\cat{Alg}_{p^r,p^s}$. Furthermore, we compute upper bounds for $\\cat{Dec}_{p^r}$ and $\\cat{Alg}_{8,2}$ over $\\ch(F)=p$ and $\\ch(F)=2$, respectively. As a result, we show $\\ed_{2}(\\cat{Alg}_{4,2})=\\ed(\\cat{Alg}_{4,2})=\\ed_{2}(\\gGL_{4}/"},"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":"1012.4877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T04:53:23Z","cross_cats_sorted":[],"title_canon_sha256":"0e3f0178a19b54752ebb47610057ac79de5d1a06eb3d14a5f4de1f8fc3ee3b6d","abstract_canon_sha256":"d5cbec68f583085f2d53b393e880edccb6b7ed72a892e67ba3b644997433657b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:45.065987Z","signature_b64":"D4JdJbOXysJhnn7A/CQpd2OKfcko0yfvD+DFTC8XN4V9+YlXx1sB0BFnArw0l2WEt2Zrv0KXk4vKeUgyihICAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e0971de18d829a3581776ea8796a8eb2a1ebcea8da2c12164caca5ba1a3f32c","last_reissued_at":"2026-05-18T04:32:45.065552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:45.065552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Essential dimension of simple algebras in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sanghoon Baek","submitted_at":"2010-12-22T04:53:23Z","abstract_excerpt":"Let $p$ be a prime integer, $1\\leq s\\leq r$ integers, $F$ a field of characteristic $p$. Let $\\cat{Dec}_{p^r}$ denote the class of the tensor product of $r$ $p$-symbols and $\\cat{Alg}_{p^r,p^s}$ denote the class of central simple algebras of degree $p^r$ and exponent dividing $p^s$. For any integers $s<r$, we find a lower bound for the essential $p$-dimension of $\\cat{Alg}_{p^r,p^s}$. Furthermore, we compute upper bounds for $\\cat{Dec}_{p^r}$ and $\\cat{Alg}_{8,2}$ over $\\ch(F)=p$ and $\\ch(F)=2$, respectively. As a result, we show $\\ed_{2}(\\cat{Alg}_{4,2})=\\ed(\\cat{Alg}_{4,2})=\\ed_{2}(\\gGL_{4}/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4877","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":"1012.4877","created_at":"2026-05-18T04:32:45.065610+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4877v1","created_at":"2026-05-18T04:32:45.065610+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4877","created_at":"2026-05-18T04:32:45.065610+00:00"},{"alias_kind":"pith_short_12","alias_value":"NYEXDXQY3AU2","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"NYEXDXQY3AU2GWAX","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"NYEXDXQY","created_at":"2026-05-18T12:26:12.377268+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/NYEXDXQY3AU2GWAXO3VIPFVI5M","json":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M.json","graph_json":"https://pith.science/api/pith-number/NYEXDXQY3AU2GWAXO3VIPFVI5M/graph.json","events_json":"https://pith.science/api/pith-number/NYEXDXQY3AU2GWAXO3VIPFVI5M/events.json","paper":"https://pith.science/paper/NYEXDXQY"},"agent_actions":{"view_html":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M","download_json":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M.json","view_paper":"https://pith.science/paper/NYEXDXQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4877&json=true","fetch_graph":"https://pith.science/api/pith-number/NYEXDXQY3AU2GWAXO3VIPFVI5M/graph.json","fetch_events":"https://pith.science/api/pith-number/NYEXDXQY3AU2GWAXO3VIPFVI5M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M/action/storage_attestation","attest_author":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M/action/author_attestation","sign_citation":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M/action/citation_signature","submit_replication":"https://pith.science/pith/NYEXDXQY3AU2GWAXO3VIPFVI5M/action/replication_record"}},"created_at":"2026-05-18T04:32:45.065610+00:00","updated_at":"2026-05-18T04:32:45.065610+00:00"}