I have an idea on quantum mechanics relevant to the collapse of the wave function and Schrodinger's cat. When a measurement is made (it is unclear to me what exactly consitutes a measuremet - but that doesn't matter). The wave function collapses and a result of the measurement happens at time t1. I think there must mow be known a new state of the wave function. Suppose there were n possible results r1, r2, ... rn of the measurement with probabilities p1, p2, ... pn. Their sum being 1.0.
The consequent paths of the wave function would differ.
But suppose there was not a measurement at time t1, but one at later time t2.
Suppose there are again n possible results s1, s2, ... sn  this time with probabilities q1, q2, ... qn.

My suggestion is that although the paths of results of the first measurement differ, the probability of the second mesurement is consistent (because quantum mechanics is linear). That is
the probability of s1
q1 is the sum of the probabilities of p1 * (s1 if r1), p2 * (s1 if r2), ... pn * (s1 if rn).
the probability of s2
q2 is the sum of the probabilities of p1 * (s2 if r1), p2 * (s2 if r2), ... pn * (s2 if rn).

by (s1 if r1) I mean probability of s1 if r1.

I think these should be theorems of quantum mechanics.

So, measurements of the life of Schrodinger's cat could be consistent, dead or alive.