Is the below sentence grammatically correct?
Know not what you know.
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Assuming that the OP is confining the analysis to imperative sentences / sentence fragments, and
Switching to a more tractable example (the original looks suspiciously like a corrupt quote (' ...he knows not what he knows...'):
Come, Lord, and tarry not.
(line from an old hymn)
Here, the archaic negative imperative is used - but the construction is just that, archaic. Except for effect / old times' sake, the regular negation ('do not tarry') (or more idiomatically, 'be quick about it') would always be chosen nowadays.
If a declarative sentence was intended, the construction is again archaic:
He knows not what to do. (archaic)
He doesn't know what to do. (modern idiomatic)