This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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ad. In an asymptotical manner, in the way of an asymptote, toward an asymptote

In an asymptotical manner; in a manner so as gradually to approach indefinitely near, though never to meet.

ad. toward an asymptote

"There have been so many events, and so many of them depend on when they occur in the time sequence, and so many of them are effectively "random" (i.e. uncorrelated) with respect to each other, that the probability of getting the same outcome with each iteration of the Phanerozoic asymptotically approaches zero."