As other astute forum members have pointed out, 25 is simply 1 / 0.04.
To the rest of the thread title though, regarding a concrete definition of financial independence:
One of MMM's biggest and best contributions to personal finance was the following, from his "Zero to Hero" post;
If you can get 25 times your annual spending saved up and working for you, that is enough to live off – forever. Don’t worry about the details – just do the saving for now
The bold is important because it keeps people from getting paralyzed between the equities vs. securities vs. real estate vs. mutual funds vs. ETFs when really, the first thing we need to do is learn how to save.
That said, all but the luckiest of us will be working for several years while we're financially independent, and during that time, I strongly encourage everyone to dig into the details and eschew hard and fast rules for what financial independence means. Of course, there is always the possibility that the future movement of US equities goes careening off the data set used in the Trinity Study, rendering the 4% rule useless. We don't think that will happen, but even if it doesn't, there are other risks that are at least as non-trivial.
If you're an American, there's a very real possibility that more legislation is passed that up-ends the path towards manageable, pre-65 healthcare costs. If you plan to become an expat, how much do you really know about the financial system of the country you're moving too?