{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HDLBVOZBGVTEUGFYCXEUS3XIJM","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":"0e229e856b7ab87f60955f1afe8fa35b4f4d884772fd697e12dfde7b0287d351","cross_cats_sorted":["math.CA","math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-29T14:30:41Z","title_canon_sha256":"fb6fa18f3e799564132dddeaf68f654f5a48410a916de47c4523e07a2e48f56d"},"schema_version":"1.0","source":{"id":"2605.31356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31356","created_at":"2026-06-01T02:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31356v1","created_at":"2026-06-01T02:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31356","created_at":"2026-06-01T02:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"HDLBVOZBGVTE","created_at":"2026-06-01T02:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"HDLBVOZBGVTEUGFY","created_at":"2026-06-01T02:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"HDLBVOZB","created_at":"2026-06-01T02:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:560308d63348034d67793895356cfa83bc1d658cfda53b8d1b4ff267566003f5","target":"graph","created_at":"2026-06-01T02:04:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.31356/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we build a bridge between the P\\'olya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the P\\'olya--Benz Theorem, classifying a central family of real-root preserving operators on the space of polynomials, as those given by $f(\\partial_z)$ for a Laguerre--P\\'olya function $f$ and the derivative operator $\\partial_{z}$. We prove that any free (additive) infinitely divisible distribution can be attained as the weak limit of root distributions of Appell polynomials $f_n(\\partial_z)z^n$ as $n\\to\\infty$, for a suitably chosen sequence $f_n$ of La","authors_text":"Andrew Campbell, Jonas Jalowy","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-29T14:30:41Z","title":"P\\'olya--Schur problems and free probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31356","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:ba4be3ffc1e384882654891de0f960d0ccf037dfc649d012fa835d770bfa3638","target":"record","created_at":"2026-06-01T02:04:00Z","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":"0e229e856b7ab87f60955f1afe8fa35b4f4d884772fd697e12dfde7b0287d351","cross_cats_sorted":["math.CA","math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-29T14:30:41Z","title_canon_sha256":"fb6fa18f3e799564132dddeaf68f654f5a48410a916de47c4523e07a2e48f56d"},"schema_version":"1.0","source":{"id":"2605.31356","kind":"arxiv","version":1}},"canonical_sha256":"38d61abb2135664a18b815c9496ee84b26ab5be6985adc26b31db25ade832e53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38d61abb2135664a18b815c9496ee84b26ab5be6985adc26b31db25ade832e53","first_computed_at":"2026-06-01T02:04:00.552287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:04:00.552287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZrO65n2w8w/oq62NEZhH+4PJSRFSI7yiaKww+h5l/N4iDMyji+5GynbB7DqkYB9DssgtVy5XHPhdudJzJYjBA==","signature_status":"signed_v1","signed_at":"2026-06-01T02:04:00.553336Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba4be3ffc1e384882654891de0f960d0ccf037dfc649d012fa835d770bfa3638","sha256:560308d63348034d67793895356cfa83bc1d658cfda53b8d1b4ff267566003f5"],"state_sha256":"037cf720e6a68484337c37fc8b9de1d6cef6d4817bbb105dee10905ded584417"}