{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OHYDNL4NUGUZXTXQDHOL6UYDWF","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":"7565cdc9a50db058a652e26fa1d31ce351204362ec17df5df114ac96301f9262","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-30T16:46:41Z","title_canon_sha256":"7685d97c74e63b534441771e87f1906f64d25202771088e57567123d00af6317"},"schema_version":"1.0","source":{"id":"1101.0111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0111","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0111v2","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0111","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"OHYDNL4NUGUZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OHYDNL4NUGUZXTXQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OHYDNL4N","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:50b7da2cb0b68a583d0d80e3be4c24d0311e276964114683c05f212a12b0a5f9","target":"graph","created_at":"2026-05-18T04:31:31Z","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":"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","authors_text":"Jeremy M. Greene","cross_cats":["math.CV","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-30T16:46:41Z","title":"Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0111","kind":"arxiv","version":2},"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":"sha256:8fcb529820b6d1051c9f3ddd8312df9263a63e6b3d48c0f934beb73da8fa8590","target":"record","created_at":"2026-05-18T04:31:31Z","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":"7565cdc9a50db058a652e26fa1d31ce351204362ec17df5df114ac96301f9262","cross_cats_sorted":["math.CV","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-30T16:46:41Z","title_canon_sha256":"7685d97c74e63b534441771e87f1906f64d25202771088e57567123d00af6317"},"schema_version":"1.0","source":{"id":"1101.0111","kind":"arxiv","version":2}},"canonical_sha256":"71f036af8da1a99bcef019dcbf5303b1552e3cfc70325e64454fbf35e1141cd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f036af8da1a99bcef019dcbf5303b1552e3cfc70325e64454fbf35e1141cd0","first_computed_at":"2026-05-18T04:31:31.977209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.977209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"93uThvda434h43FH2zWa6JikoS6XPcGKS8yDkpbno2FnnXVO/H8TiUNj2Z/fnx/g1Ek7ECr/7ADWs5b4K9zrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.977597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fcb529820b6d1051c9f3ddd8312df9263a63e6b3d48c0f934beb73da8fa8590","sha256:50b7da2cb0b68a583d0d80e3be4c24d0311e276964114683c05f212a12b0a5f9"],"state_sha256":"e843ba3fcdafe6ab72e70031f32d3debd4a223e3855ce8ad4d63a5ad9e95059a"}