{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2Y4EIONADSGZQNM2MGBHHPVXRS","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":"2298fc2c7b8c10a88c9f6ef37474f57bf3eb0a8dc4797fdcb6e7a39a2018e87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-11-30T21:56:02Z","title_canon_sha256":"80b514ec144719c4cc201bdea88792d344f03888e2a8412885177527c8693150"},"schema_version":"1.0","source":{"id":"1112.0041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0041","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0041v2","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0041","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"2Y4EIONADSGZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2Y4EIONADSGZQNM2","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2Y4EIONA","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:47ba13fdcf8d4d28f579879cbc75952df573d6ca6941d186b1003caa787fbcc5","target":"graph","created_at":"2026-05-18T03:19:33Z","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 study the existence of free subalgebras in division algebras, and prove the following general result: if $A$ is a noetherian domain which is countably generated over an uncountable algebraically closed field $k$ of characteristic 0, then either the quotient division algebra of $A$ contains a free algebra on two generators, or it is left algebraic over every maximal subfield. As an application, we prove that if $k$ is an uncountable algebraically closed field and $A$ is a finitely generated $k$-algebra that is a domain of GK-dimension strictly less than 3, then either $A$ satisfies a polynom","authors_text":"D. Rogalski, Jason P. Bell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-11-30T21:56:02Z","title":"Free subalgebras of division algebras over uncountable fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0041","kind":"arxiv","version":2},"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":"sha256:96e5104e57b45ea6778de51233f7c475050bf05c5c053f01933dfd6fb2df93ac","target":"record","created_at":"2026-05-18T03:19:33Z","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":"2298fc2c7b8c10a88c9f6ef37474f57bf3eb0a8dc4797fdcb6e7a39a2018e87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-11-30T21:56:02Z","title_canon_sha256":"80b514ec144719c4cc201bdea88792d344f03888e2a8412885177527c8693150"},"schema_version":"1.0","source":{"id":"1112.0041","kind":"arxiv","version":2}},"canonical_sha256":"d6384439a01c8d98359a618273beb78c97cdcde3b4cba2b49f9706ae2e0b86b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6384439a01c8d98359a618273beb78c97cdcde3b4cba2b49f9706ae2e0b86b7","first_computed_at":"2026-05-18T03:19:33.149181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:33.149181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpzWE9k6WMvFk+JH+WXHhi9sWUFxWLwiUX6eQLqi7IF8LR7c9Z6ErASEEYdeD55phuIjx4zF8GbRMacav76jAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:33.149816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96e5104e57b45ea6778de51233f7c475050bf05c5c053f01933dfd6fb2df93ac","sha256:47ba13fdcf8d4d28f579879cbc75952df573d6ca6941d186b1003caa787fbcc5"],"state_sha256":"6cfaa046218be70ba162b5c01c0123cd0ee33f97a55e3566d12ebbcf7ec76349"}