{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L5VRNBBIODNUV6442JV5WYAM43","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":"ebb63ed12efcc17bf601e27040bac74e6ed10e0d5bbf5415aa18aef970d511ed","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-04T12:58:38Z","title_canon_sha256":"fd96adee4ba353017062110b3238978f2378bb9a67514b6a36fea92731cb8495"},"schema_version":"1.0","source":{"id":"1403.0773","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0773","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0773v3","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0773","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"L5VRNBBIODNU","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L5VRNBBIODNUV644","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L5VRNBBI","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:72e9cdfe4eb36658f126313fc130579241c3076688cf78aeb52e2fb660926ee2","target":"graph","created_at":"2026-05-18T00:52:04Z","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":"Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \\times n$ matrix algebra is $n^2 - n + 1$ and furthermore this upper bound is attained for the so-called parabolic subalgebras. We also investigate the corresponding notion of parabolic coideals for matrix coalgebras and prove that the minimal dimension of a non-zero coideal of the matrix coalgebra ${\\mathcal M}^n (k)$ is $n-1$.","authors_text":"A.L. Agore","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-04T12:58:38Z","title":"The maximal dimension of unital subalgebras of the matrix algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0773","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":"sha256:647ad4432cf267e8e8e1cae301afe3725ed1ac51f0f1b586757d5f3497783d98","target":"record","created_at":"2026-05-18T00:52:04Z","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":"ebb63ed12efcc17bf601e27040bac74e6ed10e0d5bbf5415aa18aef970d511ed","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-04T12:58:38Z","title_canon_sha256":"fd96adee4ba353017062110b3238978f2378bb9a67514b6a36fea92731cb8495"},"schema_version":"1.0","source":{"id":"1403.0773","kind":"arxiv","version":3}},"canonical_sha256":"5f6b16842870db4afb9cd26bdb600ce6f4b76c40821db77e5a272a9cb70344ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f6b16842870db4afb9cd26bdb600ce6f4b76c40821db77e5a272a9cb70344ea","first_computed_at":"2026-05-18T00:52:04.490895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:04.490895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rEeFt5swUsWMZ357IDDUJaWCz4ad5qFyLe+47T01uDMQBOBVvTJlkcaohll81zgXbSs2TkEZ6zaROZob/AJiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:04.491433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0773","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:647ad4432cf267e8e8e1cae301afe3725ed1ac51f0f1b586757d5f3497783d98","sha256:72e9cdfe4eb36658f126313fc130579241c3076688cf78aeb52e2fb660926ee2"],"state_sha256":"f97b7f10065c2402fd442a95cdb46f61f8b0dfa79a31d0af59f3add9a1b2ea73"}