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.