Purpose of and rationale behind Go Markers U+2686 to U+2689

[Ori Avtalion]

Unicode includes the following symbols as "Go Markers":
* U+2686 ⚆ WHITE CIRCLE WITH DOT RIGHT
* U+2687 ⚇ WHITE CIRCLE WITH TWO DOTS
* U+2688 ⚈ BLACK CIRCLE WITH WHITE DOT RIGHT
* U+2689 ⚉ BLACK CIRCLE WITH TWO WHITE DOTS

It is unclear what they are for. I hope someone could explain.

1) I could not find any Go notation that uses dots inside the stones.
2) Why are there no symbols for white/black stones without dots?
3) An earlier proposal [1] suggested additional symbols:
  * GRAY CIRCLE WITH GRAY DOT RIGHT
  * GRAY CIRCLE WITH GRAY TWO DOTS
  * GRAY FILLED CIRCLE WITH WHITE DOT RIGHT
  * GRAY FILLED CIRCLE WITH WHITE TWO DOTS
what was their purpose? Any why are Go Markers proposed as
"Mathematical symbols"? Are they meant for mathematical research of
the game of Go and not for actual notation?

[1] http://www.unicode.org/L2/L2001/01067-n2318-mathadd4.pdf

Thanks in advance!