I have a stupid question. I see people all asking about time spent outside the United States as it applies for US citizenship and i'm just curious. How does immigration know the time you are out of the US. When you leave no one documents your passport that you left on a certain date. Im just curious how they verify all dates of travel

I am not positive, but I know when I enter another country they stamp my entry, and exit dates in my passport.
I think they could compute my time in USA by subtracting the time I was in a foreign country.

However, when you read these statements it is usually for the non-US citizen, and their passport would be stamped on entry and exit from USA. So, theirs would be even easier to count the time.

There are companies that sell flight passenger information, to private detectives and feds, ect. They store the info at their cost and charge big bucks.

When you leave the USA on a flight you do not pass through immigration and your passport doesn't get stamped with the an exit date.

They probably don't absolutely verify every single date. Sometimes they can use passport stamps, airline records, and similar things to track where you were, but sometimes it's possible to leave without a record. I've walked across the border to Mexico, and there was no one there who asked to check my papers.

However, if you lie or misrepresent a material fact during the naturalization process, and if they don't catch it before giving you citizenship, your naturalization may still be revoked at a later time. It's to your advantage to fill it out correctly. Let them worry about how or if they're going to check it, and rest secure in the knowledge that if they do verify it, they'll uncover data that's consistent with what you wrote.

i agree, even if they dont checked every case, this information about crossing border out and in - is just too easy to investigate and to find out truth,

so I'd never ever lie about that or anything else in N400, there are known cases of people who got Naturalized years and years ago, but then immigration finds out they lied, and deported them - like the case with former Nazi members.