You found it! I rewrote my comment like six times because I think the rigorous notation where the signal is a function of t is a little messy for a HN comment. I tried picking a notation that was less intimidating and wasn't too obviously inconsistent.
The math doesn't work, assuming scalar f, x, t1, t2 as implied by their description. For a delay the x passed at t1 has no correlation to what f calculates to. It needs vectors F(X, t) and X I think.