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The phrase "have not even" is correct and can be used in written English.
It is usually used to emphasize that something has not been done or achieved, even though it was expected or thought to be easy. It can also indicate surprise or disappointment. Here is an example sentence: I have been studying for hours, but I still have not even finished half of my homework.
Exact(59)
Many customers have not even tried.
We have not even been intimidated.
We have not even started.
Negotiations have not even begun.
"Today I have not even a toothbrush".
"I have not even preliminarily picked someone".
Some have not even applied to Howard.
We have not even tried to do so.
Error rates for newer tests have not even been established.
Keynesian economists have not even begun to answer these questions.
Many buyers have not even seen the car.
More suggestions(18)
described not even
involved not even
contributed not even
included not even
considered not even
took not even
revealed not even
representatives not even
left not even
opened not even
indicated not even
observed not even
reported not even
identified not even
represented not even
have not yet
supported not even
have never even
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com