Coming from the Latin manifestus "caught in the act," manifest can be used as an adjective or a noun as well as a verb. As an adjective, manifest is a formal way to say that something is apparent to the senses and is synonymous with evident, apparent, or clear. If you have strong feelings about something, they will be manifest on your face. A ship or plane's manifest is the list of cargo or passengers on a particular trip.
You claim that "positive thoughts always resulting in positive things" is not the basis of the LOA. In part you are correct. The foundational basis in science, as I alluded to in the article was that thought stuff particles travel through ether (not air) and interact with formless stuff to create whatever it is that you are thinking about. This was how "the law" started.