Mistaking Part Of The Finite For A Mood Adjunct [2]

Martin (2013: 54):

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To be clear, this again misunderstands not as a Mood Adjunct instead of part of the Finite do not. Again, here not is simply a formal or written variant of n't. Halliday & Matthiessen (2014: 175):

Finally, we should note that the negative word not occurs in two functions: either it is simply a formal or written variant of the Finite negative element n’t, in which case it is part of the Finite; or it is a distinct modal Adjunct in Mood or Residue. In the latter case it is phonologically salient and may also be tonic

A genuine example of not as a Mood Adjunct is

After all that, I couldn't not go, could I?