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Greene","submitted_at":"2010-12-30T16:46:41Z","abstract_excerpt":"We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it has a noncommutative complex hessian that is positive semidefinite when evaluated on open sets of matrix tuples of sufficiently large size. In this paper, we show that if a noncommutative polynomial is noncommutative plurisubharmonic on a noncommutative open set, then the polynomial is actually noncommutative plurisubharmonic everywhere and has the form p = \\sum f_j^T f_j + \\sum k_j k_j^T + F + F^T where the sums are f"},"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":"1101.0111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-30T16:46:41Z","cross_cats_sorted":["math.CV","math.FA"],"title_canon_sha256":"7685d97c74e63b534441771e87f1906f64d25202771088e57567123d00af6317","abstract_canon_sha256":"7565cdc9a50db058a652e26fa1d31ce351204362ec17df5df114ac96301f9262"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:31.977597Z","signature_b64":"93uThvda434h43FH2zWa6JikoS6XPcGKS8yDkpbno2FnnXVO/H8TiUNj2Z/fnx/g1Ek7ECr/7ADWs5b4K9zrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f036af8da1a99bcef019dcbf5303b1552e3cfc70325e64454fbf35e1141cd0","last_reissued_at":"2026-05-18T04:31:31.977209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:31.977209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.OA","authors_text":"Jeremy M. 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