{"id":"hexagon/2611.00033","pdf":"https://hexagonmath.org/pdf/2611.00033v1","url":"https://hexagonmath.org/abs/2611.00033v1","tags":["math.DS","msc:11B37","msc:11B83"],"score":0,"title":"On Bounds for Reciprocal Sums and Residues in Collatz Orbits, and Their Consequences","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Behzad Nikzad","Karl Frinkle","Fatemeh Bagherzadeh"],"reviews":0,"subject":"math.NT","summary":"We prove uniform bounds for reciprocal sums and residue products along Collatz paths. Let $\\mathcal F$ be a finite nonrepeating shortcut path whose input states are greater than $1$, let $\\mathcal R_{\\mathcal F}$ be the sum of the reciprocals of its odd inputs, and let $\\rho_{\\mathcal F}$ be its finite-path residue. Then $\\mathcal R_{\\mathcal F} 2$ is nonperiodic under the shortcut map.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}