[Yoda]

The inclined swing plane with a Vertical Hinge becomes vertical, no? The swing plane is still there or has it become something else?

There are three basic Hinge Actions that control the Clubface Motion through Impact -- Horizontal, Vertical and Angled. Horizontal Hinge Action produces a Close-Only Motion of the Clubface; Vertical produces Lay-back Only Motion; and Angled produces a Simultaneous Close-and-Lay-back Motion. Each of these Hinge Actions is produced by maintaining the Flat Left Wrist perpendicular to the associated Plane of Motion through Impact.

With the Short Shots, all three Hinge Actions can be executed in a Vertical -- not Inclined -- Plane of Motion. In other words, the Clubhead can be made to move in a Vertical Plane -- it covers the Plane Line (Up and Back Motion Only, no In) -- while the Clubface either Closes Only (Horizontal Plane of Motion) or Lays-back Only (Vertical Plane of Motion) or simultaneously Closes and Lays-back (Angled Plane of Motion). Since the Plane of the Clubhead Line of Flight is in a Vertical Plane, only one Hinge is required; namely, the Hinge that controls the Clubface alignment.

However, to respect the Inclined Plane -- to move the Clubhead Up, Back and In -- you need a Dual Hinge arrangement. That is, you need one Hinge to control the Clubface (Vertical Hinge for Layback Only or Horizontal Hinge for Close Only) and a second Hinge to control the Clubhead's Inclined Plane of Motion -- the Clubhead Line of Flight (2-N-0).

This Inclined Plane of Clubhead Motion can also be thought of as Clubshaft Control (1-L-A). So, with the Dual Hinge arrangement, the Primary Hinge would control the Clubface and the Secondary (or Strap) Hinge would control the Clubshaft (and enable it to be lowered onto the Inclined Plane). Hence, we find the Dual Horizontal and Dual Vertical Hinge Actions Variations of 10-10-D/E. There is no Dual Angled Hinge Action because only one Hinge -- the Angled Hinge -- is required to control both the Angled Plane of Clubface Motion and the Angled Plane of the Clubshaft.

Now, to your question...

The Putting Arc® discussed in this thread mandates a Clubhead Inclined Plane of Motion. Otherwise, [i]there would be no In dimension on the Backstroke and no Out Dimension on the Downstroke. Hence, the Clubhead would move in a Straight Line -- not a curved one -- and thus leave the face of the device. There would, of course, still be an Arc (unless the Clubhead was kept deliberately parallel to the ground throughout the Stroke), but it would lack the geometric Inward and Outward Dimensions of the Inclined Plane.

The Hinge Action employed must be Compatible with The Putting Arc's Inclined Plane of Motion. Thus, for other than Angled Hinging, either Dual Horizontal or Dual Vertical Hinging is required. However, if the 'hatch mark' Clubface Guides are observed (in addition to the Clubhead Arc) then the device automatically produces Angled Hinge Action. And this, as we've seen, is a single Hinge arrangement.

A final point: When we discuss Hinge Action, the Inclined Plane of Motion is presumed to exist (unless otherwise specified). Hence, in practice, the terms Horizontal Hinge Action and Vertical Hinge Action are deemed to mean Dual Horizontal and Dual Vertical.