{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NYEXDXQY3AU2GWAXO3VIPFVI5M","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":"d5cbec68f583085f2d53b393e880edccb6b7ed72a892e67ba3b644997433657b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T04:53:23Z","title_canon_sha256":"0e3f0178a19b54752ebb47610057ac79de5d1a06eb3d14a5f4de1f8fc3ee3b6d"},"schema_version":"1.0","source":{"id":"1012.4877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4877","created_at":"2026-05-18T04:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4877v1","created_at":"2026-05-18T04:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4877","created_at":"2026-05-18T04:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"NYEXDXQY3AU2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NYEXDXQY3AU2GWAX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NYEXDXQY","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:787d3b5331a0a9b90752d40f11932b0df2704d166277107ef49a16d6b8de46b2","target":"graph","created_at":"2026-05-18T04:32:45Z","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":"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}/","authors_text":"Sanghoon Baek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T04:53:23Z","title":"Essential dimension of simple algebras in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4877","kind":"arxiv","version":1},"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":"sha256:757d42bc0e0f4f4de3beb05adef85fe153aeb6e95894132f9f72bc2d88cbd150","target":"record","created_at":"2026-05-18T04:32:45Z","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":"d5cbec68f583085f2d53b393e880edccb6b7ed72a892e67ba3b644997433657b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T04:53:23Z","title_canon_sha256":"0e3f0178a19b54752ebb47610057ac79de5d1a06eb3d14a5f4de1f8fc3ee3b6d"},"schema_version":"1.0","source":{"id":"1012.4877","kind":"arxiv","version":1}},"canonical_sha256":"6e0971de18d829a3581776ea8796a8eb2a1ebcea8da2c12164caca5ba1a3f32c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e0971de18d829a3581776ea8796a8eb2a1ebcea8da2c12164caca5ba1a3f32c","first_computed_at":"2026-05-18T04:32:45.065552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:45.065552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D4JdJbOXysJhnn7A/CQpd2OKfcko0yfvD+DFTC8XN4V9+YlXx1sB0BFnArw0l2WEt2Zrv0KXk4vKeUgyihICAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:45.065987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:757d42bc0e0f4f4de3beb05adef85fe153aeb6e95894132f9f72bc2d88cbd150","sha256:787d3b5331a0a9b90752d40f11932b0df2704d166277107ef49a16d6b8de46b2"],"state_sha256":"0a07b3c2caebeb76ae439a7e0caafb2ab407f774aebcac4829fda2f6af68468d"}