3) It may be a throat clearing phrase but its inclusion is made as a precaution due to uncertainty.
I don't agree with the above statement. I think attorneys include "the invention" because everyone else does, and because it seems self-evident that your spec would talk about the invention.
I've never seen the "uncertainty" issue -- ie, is a patent without the magic word vulnerable to invalidity under 112 -- discussed before today.
However, 35 U.S.C. 112 states the specification shall contain a written description of the invention. Therefore by definition, the entire specification is "according to the invention".
No, the conclusion you draw doesn't follow the premise. If it did, there would be no such thing as a written description rejection. To the contrary, if your spec fails to describe something that's claimed -- in a way that shows the inventor "possessed" the claim at the time of filing -- you are vulnerable to a 112 written description rejection.
Another way of looking at it is that "the specification shall contain X " means "if it doesn't you're in trouble", rather than "the spec, by definition, contains X".
It would be logical that similar description could be used throughout the specification with the term "according to the invention" to focus the reader's attention on the important aspects.
As a matter of readability, I agree. But readability is only one aspect to consider when writing a patent app. Many things that improve readability can have a negative effect on claim interpretation.
Inventors explicitly describe prior art and supporting structures as such since description without could lead to rejection based on obviousness.
Not sure where you're going with the obviousness angle. I'd say that a spec that
identifies a structure as prior art would make your claim an easy 103 target, especially without an explanation of how your claim distinguishes. But I don't see why leaving out an "explicit description of prior art" would lead to a 103.
It seems explicit description of what is and what is not the invention is required.
Nah, I say that's what's required of the claims, not the spec:
35 U.S.C. 112 2nd Para.
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.