{"id":"palomar/PALOMAR-2026-10-22-000036","url":"https://github.com/wcook04/plectis-erdos-lean/tree/eb6cd7ceae9ff5c5bceeb514cac749c30861d8c6","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000036-v1.json","repo":"https://github.com/wcook04/plectis-erdos-lean","tags":["math.NT","msc:11J72","msc:11B83","msc:11R11","irrationality","reciprocal-sums","diophantine-approximation","number-theory"],"score":0,"title":"Cubic-rate irrationality for reciprocal sums","trust":"high","domain":"math.NT","source":"palomar","authors":["Will Cook"],"reviews":0,"subject":"math.NT","summary":"Every positive strictly increasing zero-indexed integer sequence a with n^3(a_n^2/a_(n+1) - 1 - 3/n) tending to zero has an irrational reciprocal sum. The entry also states the exact integer-tail and number-field steps used to exclude the resulting cubic profile: positive-density exceptions, primitive gcd reduction, square specialisation, scale twelve, forbidden words modulo seven, and regular-rate extraction. The printed one-indexed paper theorem uses its stated finite-prefix argument. The separate bounded-increment Sylvester criterion in the paper is outside this configuration, and the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"Cubic-Rate Irrationality and Reciprocal-Tail Rigidity","identifier":"https://github.com/wcook04/plectis-erdos/blob/147f3f1da400a84dcb3013ea6cef75dc8f382b09/paper/243/erdos-243-reciprocal-tail-rigidity.pdf","relationship":"formalizes"},{"title":"Reciprocal-Tail Rigidity: Theorems, Proofs and Questions","identifier":"https://github.com/wcook04/plectis-erdos/blob/147f3f1da400a84dcb3013ea6cef75dc8f382b09/paper/243/erdos243-reciprocal-tail-reasoning-surface.pdf","relationship":"formalizes"}]}