TL; DR
I have collected a bunch of definitions for the core idea of this effort, i.e., "Credibility." Each of them serves a different use.
My favorite (read: most flexibly useful) definition* is this:
Credibility is a form of validated trust.
You have it–for specific topics and with specific people–to the degree that the trust that you have already earned exceeds the trust that people must extend you for your latest ask.
The greater the ratio, the more credible you are (à la, “this should be an easy ask. After all, I have earned 10x the credibility that people need to extend to me on this ask of mine.”)
Let's look at it one element at a time.
