According to new court docs, obtained by TMZ, a judgment has been entered in Britney and Sam's divorce case ... which means they are officially no longer married or entangled as man and wife in California, something we expected after they settled up Wednesday.

Things moved fast since then obviously -- and with this latest development, it just formalizes the fact BS and SA are unattached ... however, they won't be legally single 'til later this year.

Indeed ... buried in all the paperwork -- which doesn't really contain any interesting new deets that we didn't already know -- is the fact that Britney and Sam's respective single status will not be restored until several months from now ... specifically, 7.

In other words ... Britney and Sam can't legally marry anyone else until that date -- December 2, 2024. It's a standard window in the Golden State ... each divorce has to go through a period of at least 6 months after a judgment is entered before the book closes.

As we reported ... Sam and Britney had an ironclad prenup in place -- which basically left Sam with nothing substantial. We know she agreed to pay his rent at his new place for a bit ... and while there were talks of her cutting him a check, unclear if that ever happened.

In any case ... it brings their years-long relationship to an end, and a marriage that was rife with issues too -- everything from allegations of physicality, cheating and a whole lot more.

Of course, Britney is anything but living easy right now ... her life has proven tumultuous in the aftermath of splitting up with Sam -- and even now, it appears she might be unraveling.