That's some great stuff. I'm not sure I understand it all, but I think I get the gist. Thanks!
When Gaisman developed the Probak blade in the late '20's one of his selling points was that the blade wasn't of uniform thickness. I think it was thinner in the middle with the idea being that it would flex more to better "fit" the razor but still be thick enough at the edges for keenness. Would that vary the "elastic modulus" and "bending moment"?
Elastic modulus, or Young's modulus or modulus of elasticity, is a material property. It varies little for steels. Stiffness that you feel when you bend a blade is a combination of a material's elasticity and the geometry (thickness and shape). Changing the material and/or the geometry changes the stiffness, which affects the forces or bending moments (force over distance) required to bend the blade, change the curvature, and cause deflections. Applying this to your neat question about the Probak blade, the elastic modulus would be the same for the same material, but the different shape would affect the stiffness, so the same forces applied to the edges would cause different deflections. Making the blade thinner in some spots would make the blade less stiff and easier to bend there, but making the blade thicker in other spots would make the blade stiffer and harder to bend at those spots.