This sounds interesting. There are intriguing similarities with other games: go, and Conway's "Life". It feels as if it might be quite old, with the established terminology and strategy, and the connection with Greek philosophy. I'd like to see it played.
One thought on the terminology: when I first read it, "transmutation" implied to me that stones of one type would turn into another type. It took a while for me to realise that in fact the relevant ones "died" and were removed from the board. Maybe a different word would be better here?