My sense isn't a fractional infinity, but equilibrium.

Aka, absolute.

The frame with the longest ruler and fastest clock is closest to the equilibrium of the vacuum, the unmoving void of absolute zero.

So the energy goes to infinity, while the information goes to equilibrium/zero.

Which, in practical terms, would be a fractional infinity, but that's because it's impossible to reach absolute zero. Yet that would still be the ground state of space.

So space goes from the absolute to the infinite. Zero to infinity.