Is the term "white/blank spots" in knowledge commonly used among English-speaking people?
For example: They seek to cover the "white spots" in knowledge about their state.

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I've never heard it used, though people might be able to guess what it means. It would be more natural to say:

They seek to "fill the gaps" in their knowledge about their state.

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Hi Sasha, we use the term "blind spot", this is similar to what you are referring to.