Color your beach ball

The pattern of strong charges for the three colors of quark, three antiquarks, and eight gluons (with two of zero charge overlapping).

Markov does gage theory without the translation to flat earth. Gauge is best understood has hyperbolic resolution, the angle.
I think the phycisists jumped a dimension, doing Markov trees with four rates. There is no negative and positive curvatures, just a partition between three curvatures.

I doubt they close a sphere, likely close a torus. There are two rates of curvature,in w,x,y,z. w to x and w to y.  Each of those should close. The continued fraction is now fourth degree. At low energy two of those curvatures can agree and this reverts back to a 3D system.