Very interesting question, but I saw a resolution and could not
understand why there are no contact forces between the base spheres.
thanks in advance
Here are my thoughts, though I admit they may be debatable.
I think we need to address the question in two parts. One with the upper sphere not in place and one with the upper sphere in place.
No sphere on top:
In my mind, this one is a bit tricky. We can say that the separation of the spheres from one another is "zero" if any attempt to bring them a tiny bit closer results in a "measurable" (non zero) force that tends to push them apart, and that increases rapidly the closer you attempt to bring them together. Conversely, any tiny increase in separation from this "zero" position would yield no measurable force between them. So approaching the zero separation from either direction we may consider the forces between the spheres approach zero in the limit.
We may arbitrarily define this zero separation as "touching" where the contact force is, in the limit, zero. One thought experiment would be to ask what would happen if the cylinder was removed? If there was no friction involved at any of the contacts, would the spheres separate, indicative of repulsive contact forces between them?
Sphere on top:
This is probably more straight forward. Starting with the assumption that the lower spheres are just "touching" (as defined above), clearly there will be a component of the weight of the upper sphere acting on each of the lower spheres that will tend to push the spheres apart and press them against the cylinder walls. Thus we may say that the forces between the bottom spheres should definitely be be zero due to influence of the top sphere. Once again this assumes frictionless contacts throughout.
Hope this helps.