Hausdorff dimension of Apollonian circle packing, 1.305686729, 1.305688 or yet something else?

Roberto De Leo, A conjecture on the Hausdorff dimension of attractors of real self-projective Iterated Function Systems, Experimental Mathematics 24, 270 (2015), doi:10.1080/10586458.2014.987884, using a different method, confirms the figure by Thomas & Dhar (at least the digits 1.3056867) and suggests an error in McMullen's result.

I will add this reference to the OEIS.

It seems in the meantime, there are new results:

Bai, Zai-Qiao; Finch, Steven R. Precise calculation of Hausdorff dimension of Apollonian gasket. Fractals 26 (2018), no. 4, 9 pp. claims a better approximation is

$$1.3056867280498771846459862068510\dots$$