{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7H4IE3ZCDPCFKEBSHN6WXGGMSS","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":"e078a1421bc76a8b86d5965737de452cefd0bcb05a49ecbd4f93f2afcc942b7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-14T07:44:38Z","title_canon_sha256":"8502754294627af38305d725d90e9e00900a75deb29927ed53b77a0b4b5f42a7"},"schema_version":"1.0","source":{"id":"1611.04274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04274","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04274v1","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04274","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"7H4IE3ZCDPCF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7H4IE3ZCDPCFKEBS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7H4IE3ZC","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:f932744bf75565348aa6fe0f3ef010dfc6ca2fc4024f376dd1d4377a9525e4e2","target":"graph","created_at":"2026-05-18T00:59:16Z","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 $\\mathcal{U}=\\left[\n  \\begin{array}{cc}\n  \\mathcal{A} & \\mathcal{M}\n  \\mathcal{N}& \\mathcal{B}\n  \\end{array}\n  \\right]$ be a generalized matrix ring, where $\\mathcal{A}$ and $\\mathcal{B}$ are 2-torsion free. We prove that if $\\phi :\\mathcal{U}\\rightarrow \\mathcal{U}$ is an additive mapping such that $\\phi(U)\\circ V+U\\circ \\phi(V)=0$ whenever $UV=VU=0,$ then $\\phi=\\delta+\\eta$, where $\\delta$ is a Jordan derivation and $\\eta$ is a multiplier. As its applications, we prove that the similar conclusion remains valid on full matrix algebras, unital prime rings with a nontrivial idempotent, unit","authors_text":"Jiankui Li, Jun He, Wenbo Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-14T07:44:38Z","title":"Characterizations of Jordan mappings on some rings and algebras through zero products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04274","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:c6c60ed5af590127ff617e16875916e4a07c19d636921c23cd12c1609f0599ff","target":"record","created_at":"2026-05-18T00:59:16Z","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":"e078a1421bc76a8b86d5965737de452cefd0bcb05a49ecbd4f93f2afcc942b7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-14T07:44:38Z","title_canon_sha256":"8502754294627af38305d725d90e9e00900a75deb29927ed53b77a0b4b5f42a7"},"schema_version":"1.0","source":{"id":"1611.04274","kind":"arxiv","version":1}},"canonical_sha256":"f9f8826f221bc45510323b7d6b98cc94851aca5abae02707a672960eb3969db0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9f8826f221bc45510323b7d6b98cc94851aca5abae02707a672960eb3969db0","first_computed_at":"2026-05-18T00:59:16.982275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:16.982275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uXwnO3FGbz5mfwpBQrxzK5nZcm2HR7JQeB07+MgYEQ1CGDvmKmmyftmVi/YoblQUtpwR0pd/6/YRsOWeDF54DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:16.982945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6c60ed5af590127ff617e16875916e4a07c19d636921c23cd12c1609f0599ff","sha256:f932744bf75565348aa6fe0f3ef010dfc6ca2fc4024f376dd1d4377a9525e4e2"],"state_sha256":"0563f15765485396afe8a49d736d47f91982a7c6413c537390a1d7b127647d7a"}