The contracted form not've is valid, especially among native speakers although it is uncommon in formal writing.
In fact, contracted forms are becoming increasingly popular. Just 6 days ago a member of the Stack Exchange staff posted this question
More questions from new Community VP - how'd you get started?
I had to double check that the "how'd" wasn't the contracted form of "how would" (it could've been) but of "how did". Now that's what I'd call taking liberties but it's perfectly legitimate, especially among the young and in spoken English.
Interestingly, back in 2010 the following question was posted on EL&U
Is "I'd've" proper use of the English language?
The double contracted form I'd've is a shortening of three words: I would have.
(nonstandard) I would have; I would’ve; I'd have; I woulda.
If I knew you were comin’, I’d’ve baked a cake.
But examples of double contractions are also found in the 19th century, one particularly obscure contraction is ha'p'orth, a shortening of halfpennyworth. It is recorded in a famous aphorism by The Bell’s New Weekly Messenger (London) of 12th October 1851:
We have been longing to see England and France bound together by the tie of this extraordinary cable. The long and short of it seems to be, that the rope is not long enough; and after “laying out twenty-four miles,” two-thirds of a mile remain still due to enable the rope to meet its engagements. It is a great pity that, while the manufacturers were spinning a yarn, they should have stopped short at the point of interest; and though the incident does not exactly amount to “spoiling the ship for a hap’orth of tar,” it realises the idea of injuring the metal rope for a little copper.
At some point an extra apostrophe was added to make ha'p'orth and it has since stuck.
It's worth repeating that these contractions are meant to mimic speech and are less common in formal writing.