I wanted to avoid mathematical notation and stick with natural language,
but you've convinced me that it is probably more confusing than helpful.
Anyway, my idea is really simple. I'll just repeat it one more time using
Anders Sandberg's proposed notation (see
http://www.aleph.se/Trans/Cultural/Philosophy/identity.html).
Anders defines the function dist(X,Y) to be the identity distance between
mind states X and Y as evaluated by X. For example H(X) = {Y : dist(X,Y) <
Dmax(X)} is X's maximal hull of identity, i.e., the set of states X
considers to be himself.
So what I'm saying is that dist(X,Y) equals the authenticity of Y's memory
of being X, where X is me or anyone who shares my (still tentative)
philosophy of personal identity.