{"paper":{"title":"What to Expect When You're Expecting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mark Whitmeyer","submitted_at":"2026-06-29T14:47:21Z","abstract_excerpt":"The marginal degree of sums in dimension \\(n\\) is the smallest integer \\(k\\) such that the joint distributions of all subcollections of at most \\(k\\) coordinates of a real-valued random vector \\(\\left(X_1,\\ldots,X_n\\right)\\) determine the value of \\(\\E\\left(X_1+\\cdots+X_n\\right)\\), whenever this expectation is defined. For every \\(n\\ge2\\), we prove that this marginal degree is \\(\\left\\lceil n/2\\right\\rceil\\). The upper bound follows from a theorem of Simons (1977). The lower bound is proved by constructing, for every \\(1\\le k<\\left\\lceil n/2\\right\\rceil\\), two joint laws whose marginals of dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30400","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/2606.30400/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"}