What is MIP hypothesis? While reading about muon analysis I read that finding calorimetry segments

The relationship between the energy detected in (a large class of) ionizing detectors and the distance traveled depends a bit on the energy of the particle, but the curve has a valley and is only weakly sensitive to speed in that valley (and the speed of minimum ionization also depends on the particle mass).
The rate of energy deposition for particles at the bottom of the valley is called 'minimum ionization'.
A minimum ionizing particle (MIP) is one that has the speed that generate minimum ionization.
The hypothesis here is that the track length is connected to the detector response by the assumption that the particle's speed is in the valley. So this is a analysis method (rather than a result you are hoping to publish) that works by saying
"Assume [some fact] about the thing we've detected and use that to work out more details, then later we'll look to see if the fit that results is consistent with what we assumed."
And because the minimium ionization valley is pretty broad and a lot of particles are roughly qualified this works out very well.