An Oriented Finite-Spin Vertex with Retained Tetrahedral Geometry: construction, canonical measure, and the gluing obstruction
We construct a finite-spin, orientation-resolved four-simplex vertex amplitude that retains the full tetrahedral intertwiner algebra. Orientation is selected by restricting the history integration to the domain on which a native Spin(4)-invariant pseudoscalar has fixed sign. Because the restriction acts on the integrat...