{"id":"hexagon/2610.00340","pdf":"https://hexagonmath.org/pdf/2610.00340v1","url":"https://hexagonmath.org/abs/2610.00340v1","tags":["math.QA","msc:57K16","msc:13A30","msc:13J10","Habiro cap","Hopf pairing","Morita sewing","Rees completion","root of unity"],"score":0,"title":"Integral root fibers and closed factorizations: Pairing maps, Rees covariance, caps, and sewing","domain":"math.GT","origin":"ai-generated","source":"hexagon","authors":["Hao-Yu Sun"],"reviews":0,"subject":"math.GT","summary":"We construct rootwise and formal Rees boundary data from the marked modules and lattices of the companion boundary-module construction, keeping their distinct coefficient and completion domains. Using a Newton interpolation basis, we determine the Smith invariants and the integral image of the map induced by the Hopf pairing. Factorial/Rees covariance and compatible finite-stage representatives produce a strict rootwise/Rees module with its theta endpoint. At an admissible odd prime, no continuous homomorphism extends algebraic root specialization to the entire completed Rees source; further…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex","Mathematica"],"discussed":0,"published":"2026-10-18","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}