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We say that $d=\\{d_n: n\\in N\\}$ is a Jordan higher derivable mapping at a given point $G$ if $d_{n}(ST+ST)=\\sum\\limits_{i+j=n}\\{d_{i}(S)d_{j}(T)+d_{j}(T)d_{i}(S)\\}$ for any $S,T\\in Alg \\mathcal{N}$ with $ST=G$. An element $G\\in Alg \\mathcal{N}$ is called a Jordan higher all-derivable point if every Jordan higher derivable mapping at $G$ is a higher derivation. In this paper, we mainly prove that any given point $G$ of Alg$\\mat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.5590","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-23T14:11:27Z","cross_cats_sorted":[],"title_canon_sha256":"ef6a3f3dc14e958c0f6caad2962b7a038c69074ebf98e0fdf65628c9441d9430","abstract_canon_sha256":"9fef54fcd18eefdf7fa7313553222735995d6c93a980b378fbd0ed3b46ae4576"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:46.474190Z","signature_b64":"oL4lkuSC0HMUTn8Y6SR98W3ou+i7+OoZaIi4C4qXmz6w2RJAegguuUuz3xWoAoiCXibSoMr9FGQMBmxNHMtWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90e6d9a8730c721fdb53cd0c5ea4c5295e122019323062eb95616cbec30931ca","last_reissued_at":"2026-05-18T04:05:46.473819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:46.473819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Jordan Higher All-Derivable Points in Nest Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jun Zhu, Nannan Zhen","submitted_at":"2011-12-23T14:11:27Z","abstract_excerpt":"Let $\\mathcal{N}$ be a non-trivial and complete nest on a Hilbert space $H$. Suppose $d=\\{d_n: n\\in N\\}$ is a group of linear mappings from Alg$\\mathcal{N}$ into itself. We say that $d=\\{d_n: n\\in N\\}$ is a Jordan higher derivable mapping at a given point $G$ if $d_{n}(ST+ST)=\\sum\\limits_{i+j=n}\\{d_{i}(S)d_{j}(T)+d_{j}(T)d_{i}(S)\\}$ for any $S,T\\in Alg \\mathcal{N}$ with $ST=G$. An element $G\\in Alg \\mathcal{N}$ is called a Jordan higher all-derivable point if every Jordan higher derivable mapping at $G$ is a higher derivation. 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