Corollary: Peripheral reduction in this presentation

After the realized geometry, overlap components, charts, and seam have been fixed, every closed word is determined by its winding through (eq:word). Regular words have winding zero and one primitive meridian determines all peripheral powers. Core/collar agreement must still be checked in the same transported frame.

Proof. Equation (eq:word) gives the first two assertions. The punctured cone is topologically a punctured plane; angular lifting identifies its loop classes with integer winding. The core and collar checks are the two explicit winding-one words of Lemma lem:holonomy.