Vanishing Einstein spectral functional for suitably regular spectral triples of dimension 2

Let $({\mathcal A},D,{\mathcal H})$ be a suitably regular spectral triple of dimension $2$, and let the Einstein spectral functional be the functional introduced in the paper from this spectral triple.

Vanishing Einstein functional conjecture. The Einstein spectral functional vanishes.

This is proposed as a direction for further computation, motivated by the expectation that the spectral Einstein functional should vanish for more general spectral triples over noncommutative two-tori. The statement is presented as an expectation rather than established result.