Was Nicki Minaj-Mariah Carey fight faked for ‘Idol’ publicity?

Fox hit the mother lode Wednesday when video of one new “American Idol” judge attacking another new “Idol” judge got leaked to the media.

And if Nicki Minaj — you guessed that, right? — actually did suggest, as one report claims, that if she had a gun, she would shoot Mariah Carey . . . well, you can’t make an omelet without breaking some eggs.

And by “omelet,” we mean the inordinate amount of chatter on television, online and in the social ether Wednesday for a singing-competition series that last season suffered its smallest numbers since its summer 2002 launch — and that isn’t even scheduled to return to Fox’s lineup for three more months.

Fox and the show’s producers declined to take credit for, or comment on, what many assumed was a brilliantly orchestrated publicity stunt. They’re being too modest; at the very least, they deserve full credit for so quickly realizing the upside of their decision to put crazy + crazy together on the new “Idol” judging panel.

“Could you please place a ‘paid advertisement’ warning on these types of stories?” asked someone in the tsunami of Web comments about the “Idol” judge dust-up, adding: “This is OBVIOUSLY a manufactured feud for ratings.”

“Don’t watch the show but it seems it is all about the judges and not about the singers anymore. Is that correct?” weighed in another commenter.

“Idol” exec producer Nigel Lythgoe insisted that the report of Minaj threatening Carey with physical harm is “absolute rubbish.” This he knows, he said, because “Mariah confronted Nicki” on Wednesday morning and asked whether she made the death threat Tuesday and “Nicki said, ‘Absolutely not.’ ”

Carey’s people are “stirring the pot and gave her bad info,” Lythgoe told TMZ — “Idol’s” 

“in-house” publicity machine — where the singing competition every season sends its Idolettes for on-camera paparazzi training.

Were Carey not in the auditions room when Minaj was ranting, and getting all her information secondhand, Lythgoe’s comments might make sense. But Carey was in the room, as seen in the video, with only skinny Keith Urban separating her from Minaj. Lythgoe was there, too; you can see him in the video, which first turned up on — you know it’s coming — TMZ.

In the video — from auditions in Charlotte on Tuesday — Minaj is seen sitting at a far end of the judges’ table, where Steven Tyler sat the past two seasons. Next to her sits Urban, and Carey sits on his other side, followed by Randy Jackson, the only returning judge, who’s in the chair he has occupied since Simon Cowell left the show.

Minaj and Carey exchange words after disagreeing about an auditioner’s performance — at the end of a long day of tryouts, show host Ryan Seacrest noted Wednesday morning on his syndicated radio show.

“Think I’m playin’? Think this [expletive] is a [expletive] joke?” Minaj is heard saying.

After then saying “think it’s a joke?” two times, she added: “If you say one more disrespectful thing to me — off with your head!”

“TIME OUT! TIME OUT!” Jackson began to shriek.