{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2ZKBT2YKW6J5GK6XMF2GRQPBIY","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":"f9c9c7478f159494a477292c6bf379be438df74e46639ddd0911200a7a83e6ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-03T10:24:32Z","title_canon_sha256":"a36cfdb3da936ee60c61301e12dcfa01b9fc74f3031d5e9a70610160b20dca68"},"schema_version":"1.0","source":{"id":"1402.0332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0332","created_at":"2026-05-18T03:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0332v1","created_at":"2026-05-18T03:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0332","created_at":"2026-05-18T03:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"2ZKBT2YKW6J5","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2ZKBT2YKW6J5GK6X","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2ZKBT2YK","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:6b9244050be49065400a49913c99d55b4b42109c7930e3c5da235b91e929781d","target":"graph","created_at":"2026-05-18T03:00:23Z","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 bound the symbol length of elements in the Brauer group of a field $K$ containing a $C_m$ field (for example any field containing an algebraically closed field or a finite field), and solve the local exponent-index problem for a $C_m$ field $F$. In particular, for a $C_m$ field $F$, we show that every $F$ central simple algebra of exponent $p^t$ is similar to the tensor product of at most $len(p^t,F)\\leq t(p^{m-1}-1)$ symbol algebras of degree $p^t$. We then use this bound on the symbol length to show that the index of such algebras is bounded by $(p^t)^{(p^{m-1}-1)}$, which in turn gives a","authors_text":"Eliyahu Matzri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-03T10:24:32Z","title":"Symbol length in the Brauer group of a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0332","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:ef0c650b823c9714bb748b8ef6611ba080032cbeaf657b39a07c6bab3dc1f4e8","target":"record","created_at":"2026-05-18T03:00:23Z","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":"f9c9c7478f159494a477292c6bf379be438df74e46639ddd0911200a7a83e6ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-02-03T10:24:32Z","title_canon_sha256":"a36cfdb3da936ee60c61301e12dcfa01b9fc74f3031d5e9a70610160b20dca68"},"schema_version":"1.0","source":{"id":"1402.0332","kind":"arxiv","version":1}},"canonical_sha256":"d65419eb0ab793d32bd7617468c1e14622f82a5f73ce956f8c11579cf33110cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d65419eb0ab793d32bd7617468c1e14622f82a5f73ce956f8c11579cf33110cf","first_computed_at":"2026-05-18T03:00:23.840131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:23.840131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"reeDlieo4iwtMTnc+7aU0O9yqWpNMhzqHMKjSfPSDLVSP9idchbu0IKMBxFVXkf63Ctr8xNgMJndvQjVH+ydDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:23.840988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef0c650b823c9714bb748b8ef6611ba080032cbeaf657b39a07c6bab3dc1f4e8","sha256:6b9244050be49065400a49913c99d55b4b42109c7930e3c5da235b91e929781d"],"state_sha256":"32e6f8fc92091f12c40bea30294790720b91a53647af7de51efa67baf8e45725"}