I created a short video with my smartphone to demonstrate how to easily detect a downward-bowed pan warp. On a hard, level surface, such as the granite tile in the video, the pan will rock or "wobble", as collectors like to say. By pressing on the rim of the pan at various points, you can feel and see the movement, and listen for the clicking sounds that are tell-tale signs of warping. At the end of the video, you can also see why collectors call such pans "spinners".
Here's a short video showing electrolysis cleaning in action:
The numerals on older cast iron pieces do not indicate the diameter, but rather what size woodstove eye the pan would fit.