{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MWDSZIJPIB7UBRUTSGVKQ4MA7Z","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":"3add52f92d3e68790ac835bb28a085c90e87f1666a7264b72c0db453b87db45b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-01T21:23:19Z","title_canon_sha256":"8647f3343380fd46a0f25e4800fddd2c591cffb9eb32ea2c7b2779a0372b4a44"},"schema_version":"1.0","source":{"id":"1507.00377","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00377","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00377v3","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00377","created_at":"2026-05-18T00:47:51Z"},{"alias_kind":"pith_short_12","alias_value":"MWDSZIJPIB7U","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWDSZIJPIB7UBRUT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWDSZIJP","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:fb1745a8dac83336ba62c4596a9afe3e02425e9ac696c57975c8b6cdf21a67c4","target":"graph","created_at":"2026-05-18T00:47:51Z","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 approach celebrated theorems of Burnside and Wedderburn via simultaneous triangularization. First, for a general field $F$, we prove that $M_n(F)$ is the only irrreducible subalgebra of triangularizable matrices in $M_n(F)$ provided such a subalgebra exists. This provides a slight generalization of a well-known theorem of Burnside. Next, for a given $n > 1$, we characterize all fields $F$ such that Burnside's Theorem holds in $M_n(F)$, i.e., $M_n(F)$ is the only irreducible subalgebra of itself. In fact, for a subfield $F$ of the center of a division ring $D$, our simple proof of the aforem","authors_text":"Bamdad R. Yahaghi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-01T21:23:19Z","title":"Theorems of Burnside and Wedderburn revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00377","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":"sha256:1b6bb1ed2aafb45e43ebeef006f1bd201d95e22924d29061f15db8363a72f4a8","target":"record","created_at":"2026-05-18T00:47:51Z","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":"3add52f92d3e68790ac835bb28a085c90e87f1666a7264b72c0db453b87db45b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-01T21:23:19Z","title_canon_sha256":"8647f3343380fd46a0f25e4800fddd2c591cffb9eb32ea2c7b2779a0372b4a44"},"schema_version":"1.0","source":{"id":"1507.00377","kind":"arxiv","version":3}},"canonical_sha256":"65872ca12f407f40c69391aaa87180fe6ae6dea1545e821c8fd7e5d30a34d118","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65872ca12f407f40c69391aaa87180fe6ae6dea1545e821c8fd7e5d30a34d118","first_computed_at":"2026-05-18T00:47:51.322129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:51.322129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6UPYuCuu2tR/xpa7FBw1lw+tUwvaAk8stBohFL8XCdGyla645Z+FftLsQxJvXuel+auMBmraaDfRSE+VHHQPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:51.322919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00377","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b6bb1ed2aafb45e43ebeef006f1bd201d95e22924d29061f15db8363a72f4a8","sha256:fb1745a8dac83336ba62c4596a9afe3e02425e9ac696c57975c8b6cdf21a67c4"],"state_sha256":"f6a37157b05b6f9cdb892f879ebac8f05dee2986c5eaca42f8aa933e8c775d47"}