{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2TUMOV2NPTQVPSNIQXHGBBEJIE","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":"0c01331a3e834e4572f0299ff25f77e61493f9aacbc96f8a17dfdacbc0bd519c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-12T13:30:37Z","title_canon_sha256":"1ce6de5811b47f374eaf9fdfbcff646616d7c19590e396a196e6f9875d001704"},"schema_version":"1.0","source":{"id":"1202.2527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2527","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2527v1","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2527","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"2TUMOV2NPTQV","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2TUMOV2NPTQVPSNI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2TUMOV2N","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:e8f507bf9a1dcc36a3d8d07b719f31343f2333c2651c26894fc2ff29a096bae0","target":"graph","created_at":"2026-05-18T04:02:26Z","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 $\\mathcal{G}=[A & M   N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, \\Phi_{MN}, \\Psi_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the generalized matrix algebra $\\mathcal{G}$. It is shown that if one of the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ is nondegenerate, then every antiderivation of $\\mathcal{G}$ is zero. Furthermore, if the bilinear pairings $\\Phi_{MN}$ and $\\Psi_{NM}$ are both zero, then every Jordan derivation of $\\mathcal{G}$ is the sum of a derivation and an antideri","authors_text":"Feng Wei, Leon van Wyk, Yanbo Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-12T13:30:37Z","title":"Jordan Derivations and Antiderivations of Generalized Matrix Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2527","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":"sha256:57a0e0943f357590f760d3a2b89e990bbc29e080a72bb8bbfb07bd34e532021b","target":"record","created_at":"2026-05-18T04:02:26Z","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":"0c01331a3e834e4572f0299ff25f77e61493f9aacbc96f8a17dfdacbc0bd519c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-02-12T13:30:37Z","title_canon_sha256":"1ce6de5811b47f374eaf9fdfbcff646616d7c19590e396a196e6f9875d001704"},"schema_version":"1.0","source":{"id":"1202.2527","kind":"arxiv","version":1}},"canonical_sha256":"d4e8c7574d7ce157c9a885ce608489411af12b82de51eddbbc2501533718508a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4e8c7574d7ce157c9a885ce608489411af12b82de51eddbbc2501533718508a","first_computed_at":"2026-05-18T04:02:26.278679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.278679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OqjlJniYW315rFqbhjL98zPGSoXs7AO+xh+Onz6YfoCukBuTPxikp1J5GCEtZpNVaP3YBGh1A0fRVWgNTnRFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.279271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a0e0943f357590f760d3a2b89e990bbc29e080a72bb8bbfb07bd34e532021b","sha256:e8f507bf9a1dcc36a3d8d07b719f31343f2333c2651c26894fc2ff29a096bae0"],"state_sha256":"6f0d5948cbb31b0ae3bc37cbea8f866bda0e389f0f381d692451c0af1fbe21f7"}