{"paper":{"title":"Sums of finitely many distinct rationals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Hobby, Donald Silberger, Sylvia Silberger","submitted_at":"2017-02-04T17:56:04Z","abstract_excerpt":"${\\cal E}$ denotes the family of all finite nonempty $S\\subseteq{\\mathbb N}:=\\{1,2,\\ldots\\}$, and ${\\cal E}(X):={\\cal E}\\cap\\{S:S\\subseteq X\\}$ when $X\\subseteq{\\mathbb N}$. Similarly, ${\\cal F}$ denotes the family of all finite nonempty $T\\subseteq{\\mathbb Q}^+$, and ${\\cal F}(Y) := {\\cal F}\\cap\\{T:T\\subseteq Y\\}$ where ${\\mathbb Q}^+$ is the set of all positive rationals and $Y\\subseteq{\\mathbb Q}^+$.\n  This paper treats the functions $\\sigma:{\\cal E}\\rightarrow{\\mathbb Q}^+$ given by $\\sigma:S\\mapsto\\sigma S :=\\sum\\{1/x:x\\in S\\}$, the function $\\delta:{\\cal E}\\rightarrow{\\mathbb N}$ defined"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01316","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":""},"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"}