I'm getting really tired of your using the Socratic method to get me to explain the obvious. But last round.
You say electromagnetic interactions dissapear at any significant distance, yet they are responsible for holding materials together?
There is essentially no direct attraction between distant atoms, but nothing stops you from having a line of atoms, each of which attracts the next.
Consider the case of a piece of glass. I am saying that electromagnetic forces hold the glass together. But those forces only exist between atoms that are in close proximity. However one atom holds on to the next holds on to the next through the whole glass, and it acts like a single rigid object.
However if you take that piece of glass and shatter it, you've separated the atoms along the cracks and they do not attract each other. In theory you should be able to put the pieces together and the crack will mend. In practice you simply can't put the pieces of glass closely enough together. (But The Feynman Lectures on Physics explains how sliding a piece of wet glass past a piece of wet glass does result in small portions mending then breaking, resulting in scratches on the glass. The water is necessary to lift surface impurities to allow pure connections to form.)
The necessary condition for rigidity (disregarding amorphous solids) is crystalline microstructure.
And what causes that crystalline microstructure other than the pattern of positive and negative charges on the atoms involved, resulting in adjacent atoms being attracted to each other?
Anyways as I've said, I've had enough of your drawing out rounds with asking questions that I am sure you know the answer to. Therefore if your next response isn't rather extraordinary, I'll be leaving this conversation.