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Katie Holmes Taping SYTYCD Performance in L.A. Today

Katie Holmes is taping her guest appearance for So You Think You Can Dance today, a source tells

The actress was spotted arriving at a sound stage on the CBS Studio lot — where STYCD airs live each week — this morning.

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"They are making it seem like a huge Broadway production," the source tells Us. "It's a massive set." After taping there, Holmes is due to head over to FOX Studios to continue taping on a New York set.

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Holmes — who was also spotted rehearsing at CBS Studios yesterday — "has been working on this for a long time," the source says. "She is working with the choreographer Tyce Diorio. They want it to seem like she waltzed in and put it together very quickly, but that's really not the case. This has been a longtime in the making."

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The actress — who also danced during a guest appearance on Eli Stone — "is killing it," the source goes on. "She looks incredible. She is just doing an amazing job. Everyone is absolutely floored by how talented she is." Her performance "might broadcast this week as news has started to leak out — but they're trying to save it for July 8th, as that is the 100th episode," the source reveals.

Producer and judge Nigel Lythgoe told Us earlier that he'd "love" to have Holmes on the show. "As far as I'm concerned, Katie Holmes can come on the show and do anything she'd like to do," he said without confirming her appearance. "I'm not making any comments at this point," he told Us. "It is just a rumor for now."

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