The Skwedge Disparity: Volumetric Ambiguity in Underdetermined Circle-to-Line Lofts

The transition from a circular base to a finite apex line segment (typically a Loft(Circle, Line) operation) constitutes a dimensional degeneration in boundary-representation modeling. This transition is underdetermined: the boundary data fail Hadamard's uniqueness criterion, admitting a continuous family of topologically valid solids. We formally introduce the Skwedge as a geometric genus containing three distinct canonical species: Skwedge curvum (the ruled Right Conoid), Skwedge convexum (the Convex Hull), and Skwedge projectivum (the Projective Maximum). While CAD kernels often default to implicit smoothing approximations, we show that strictly enforcing orthogonal projection constraints admits a solution space where the volume varies significantly. We quantify the "Skwedge Disparity" (the volumetric error between the ruled baseline and the projective maximum) as 15.12% relative to the ruled proxy and 13.13% relative to the admissible maximum. This gap represents an irreducible volumetric uncertainty in any application relying on default CAD lofts without explicit species selection.