{"paper":{"title":"Repeated differentiation of deterministic polynomials with asymptotically radial root distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"Brian C. Hall, Daniel Perales","submitted_at":"2026-07-18T20:11:58Z","abstract_excerpt":"Recent works of Galligo, Najnudel, and Vu (2025) and Najnudel and Vu (2026) study repeated differentiation for polynomials of the form $P(z)=p(z^m)$, where $p$ is a deterministic polynomial of degree $n$ with real, non-negative roots, in the regime where $m$ and $n$ are large. If $m\\gg \\log(n)$ and the root distribution of $P$ converges to a compactly supported, radial probability measure $\\mu_0$, these works show that for $0\\le t<1$, the root distribution of the $\\lfloor nmt\\rfloor$-th derivative of $P$ converges to a compactly supported probability measure $\\mu_t$ given by an explicit formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16954","kind":"arxiv","version":1},"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/2607.16954/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"}