The reason why I offer $1M to anybody that can disprove my axiom, &c, is as follows:
It is very simple to model a One-way Crush down process. Take an object A and put in on the ground and then another object C. You drop C on A and A is crushed.
Why is that?
If C can apply suffient energy PE at impact C with A and following downward displacement and total strain energy SE that can be absorbed by A+C is less than PE and that C can absorb more strain energy than A and only deform elastically in the process, then A is crushed and C is not.
It is not really 'one-way' as C is always affected - elastic deformation - but it is pretty near.
I would conclude that 'one-way' crush down is only possible, if C can absorb more strain energy only as elastic deformation than A can absorb totally (elastic & plastic deformation, failures, &c).
If C is then only 1/10th of A volume/mass wise - as per Challenge conditions - and can only absorb 1/10th of A strain energy (A and C have same internal structure), then I would conclude C can never crush A in any model, size or scale.
It is just a question of strain energies! C has too little!
The Challenge is to prove me wrong!