Agreed.

When I opened the paper, I thought they were talking about an elementary function closed-form solution. I thought “Wow, what math sorcery did they use for that !”. Then I read it and they created a provably tight approximation. Good enough to use and computationally efficient. But not the same as a true math solution.

From the paper:

“To approach this problem, we discretize I(s) into piecewise constant segments and obtain the discrete approximation of the integral in terms of the sum of piecewise constant compartments over intervals. This piecewise constant approximation inspired us to introduce an approximate closed-form solution for the integral that is provably tight when the integral appears as the exponent of an exponential decay, which is the case for LTCs. We theoretically justify how this closed-form solution represents LTCs’ ODE semantics and is as expressive (Fig. 1).”

Not quite a math solution, but a great accomplishment if it performs as well as they hope.