{"id":"hexagon/2610.00276","pdf":"https://hexagonmath.org/pdf/2610.00276v1","url":"https://hexagonmath.org/abs/2610.00276v1","tags":["math.QA","msc:57K16","msc:57K30","msc:57K20","anomaly normalization","fixed-level transport","handleslide coherence","skein module","topological quantum field theory"],"score":0,"title":"Fixed-Level TQFT Transport of Marked Handleslide Coherence: Disjoint Cubes and a Three-Handle Pentagon","domain":"math.GT","origin":"ai-generated","source":"hexagon","authors":["Hao-Yu Sun"],"reviews":0,"subject":"math.GT","summary":"Fix an ordinary level $K\\geq1$ and a fully specified family of pairwise disjoint positive handleslides on a compression body. The main question is how a literal geometric relation becomes a literal finite-level operator relation. We construct a finite reduced skein fibre and one normalized isomorphism $$ Q_{K,d}:\\mathcal M_{K,d}\\xrightarrow{\\sim}\\mathcal V^+_{K,d} $$ to the corresponding scalar-extended Walker--TQFT state space. Reusing this map at every vertex sends the supplied weight-zero slide cylinders to $E_K$-linear automorphisms: geometric squares become operator squares, finite…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}