{"paper":{"title":"Radial Transform Extremality for the Siblings of the Coupon Collector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christopher D. Long","submitted_at":"2026-06-30T09:19:30Z","abstract_excerpt":"In the siblings version of the coupon collector, a main collector stops when every coupon type has appeared once. Duplicates are passed successively to siblings, and $U_j^N$ denotes the number of empty spaces in the $j$th collector's album at the main completion time. We prove finite-$N$ radial transform strengthenings of the uniform-probability extremality principle. For every $N\\ge2$, every $j\\ge2$, every positive nonuniform probability vector $p$, and the ray $p(\\theta)=u+\\theta(p-u)$ from the uniform vector $u$, the full probability generating function $\\mathbb{E}_{p(\\theta)}z^{U_j^N}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31391","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/2606.31391/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"}