{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PMAVD2BDV55OV7N3FC4TVIBW2R","short_pith_number":"pith:PMAVD2BD","schema_version":"1.0","canonical_sha256":"7b0151e823af7aeafdbb28b93aa036d47b7a4044c22bdd7279d5a7ba20385210","source":{"kind":"arxiv","id":"2512.23528","version":2},"attestation_state":"computed","paper":{"title":"On the Brown measure of $x + i y$, with $x,y$ selfadjoint and $y$ free Poisson","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Alexandru Nica, Franz Lehner, Kamil Szpojankowski, Ping Zhong","submitted_at":"2025-12-29T15:06:59Z","abstract_excerpt":"Let $x,y$ be freely independent selfadjoint elements in a $W^{*}$-probability space, where $y$ has free Poisson distribution of parameter $p$. We pursue a methodology for computing the absolutely continuous part of the Brown measure of $x + i y$, which relies on the matrix-valued subordination function $\\Omega$ of the Hermitization of $x + i y$, and on the fact that $\\Omega$ has an explicitly described left inverse $H$. Our main point is that the Brown measure of $x + i y$ becomes more approachable when it is reparametrized via a certain change of variable $h : \\mathcal{D} \\to \\mathcal{M}$, wi"},"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":"2512.23528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-12-29T15:06:59Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"3f404dac815504b23ef1e97151a245169d3dc4dbd2ac3b51ebced2110c1ea8d2","abstract_canon_sha256":"d4867e8b255ef9eb80430e784effbe88cf8322571714e31baa920e59075a5873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:41.853733Z","signature_b64":"KsGQvS2DFPcFJmTZCM5uch6f44pYZX5Im4qo5DXcqsZ5DstED0WwAs1njiiz3kbG9/3oFjYdkeuKz0+rejPXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b0151e823af7aeafdbb28b93aa036d47b7a4044c22bdd7279d5a7ba20385210","last_reissued_at":"2026-05-27T01:05:41.852961Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:41.852961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Brown measure of $x + i y$, with $x,y$ selfadjoint and $y$ free Poisson","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.OA","authors_text":"Alexandru Nica, Franz Lehner, Kamil Szpojankowski, Ping Zhong","submitted_at":"2025-12-29T15:06:59Z","abstract_excerpt":"Let $x,y$ be freely independent selfadjoint elements in a $W^{*}$-probability space, where $y$ has free Poisson distribution of parameter $p$. We pursue a methodology for computing the absolutely continuous part of the Brown measure of $x + i y$, which relies on the matrix-valued subordination function $\\Omega$ of the Hermitization of $x + i y$, and on the fact that $\\Omega$ has an explicitly described left inverse $H$. Our main point is that the Brown measure of $x + i y$ becomes more approachable when it is reparametrized via a certain change of variable $h : \\mathcal{D} \\to \\mathcal{M}$, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.23528","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.23528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.23528","created_at":"2026-05-27T01:05:41.853048+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.23528v2","created_at":"2026-05-27T01:05:41.853048+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.23528","created_at":"2026-05-27T01:05:41.853048+00:00"},{"alias_kind":"pith_short_12","alias_value":"PMAVD2BDV55O","created_at":"2026-05-27T01:05:41.853048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PMAVD2BDV55OV7N3","created_at":"2026-05-27T01:05:41.853048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PMAVD2BD","created_at":"2026-05-27T01:05:41.853048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R","json":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R.json","graph_json":"https://pith.science/api/pith-number/PMAVD2BDV55OV7N3FC4TVIBW2R/graph.json","events_json":"https://pith.science/api/pith-number/PMAVD2BDV55OV7N3FC4TVIBW2R/events.json","paper":"https://pith.science/paper/PMAVD2BD"},"agent_actions":{"view_html":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R","download_json":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R.json","view_paper":"https://pith.science/paper/PMAVD2BD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.23528&json=true","fetch_graph":"https://pith.science/api/pith-number/PMAVD2BDV55OV7N3FC4TVIBW2R/graph.json","fetch_events":"https://pith.science/api/pith-number/PMAVD2BDV55OV7N3FC4TVIBW2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R/action/storage_attestation","attest_author":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R/action/author_attestation","sign_citation":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R/action/citation_signature","submit_replication":"https://pith.science/pith/PMAVD2BDV55OV7N3FC4TVIBW2R/action/replication_record"}},"created_at":"2026-05-27T01:05:41.853048+00:00","updated_at":"2026-05-27T01:05:41.853048+00:00"}