Re: "it doesn't seem to specify..."

Charles,

by "it" are you referring to the substance of the talk on Samsara? (and to 'wandering on') Rhetorial question.

On that same site, (just for example) there are many good things to read and hear about "stopping the process". Basically, I think you can sum up the process/specifics this way, though the language might differ, depending on the path:

Recognition is awakening.
Awakening *IS many levels.

(*Awakening is an active 'being state',
not an accoutrement, or an acquirement, as in "have/has".)

Thought is based on perception.
No thought is neutral.
Meditation is disengagement from thought:
it is neither negative nor positive.
It is the middle path
and it includes the dissolution of karma--(the undoing of Samsara)
by being aware and not engaging
in positive or negative.

All the various practises have to do with training the mind
not to think, but to recognize.

Thinking is perceiving.
Recognition is awakening.

I hope that answers your question, or at the least, leaves question
worth deeply considering. :-)

re: the language. Karma is a complex subject,
and one very little understood, though the word is much parroted.
It's worth looking into.