A Pivot-Independent Toric Model for Framed Carlsson-Weinshall Duality

An ordered projective anchor simplex and \(n\) further marks in its complement determine a configuration torus modulo diagonal translation. Choosing a pivot mark identifies this quotient with a product of tori, which has a product-permutohedral compactification. We construct a pivot-independent normal projective model dominating all these compactifications. Its fan is the arrangement of rectangle characters, or equivalently the normal fan of an explicit lattice zonotope. Inversion extends regularly; in dimension three it gives a biregular Carlsson-Weinshall duality on the closures of the reduced-measurement graphs. For ambient dimension \(d\ge 1\) and \(n\ge 2\) marks, the common model is smooth exactly when \(d=1\) or \(n=2\). Otherwise it contains a four-dimensional cone with five extreme rays and is not \(\mathbb Q\)-factorial. Classical CW duality and standard toric machinery are credited. This is a complete theorem about the specified anchor-framed model, not a stable compactification of unframed camera moduli or a full closure of AIM Algebraic Vision Problem 5.3. AI-assisted, self-audited and unrefereed; no absolute-priority claim is made.