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jack-dorsey-demoTwitter co-founder Jack Dorsey has returned to active duty at Twitter and is involved in “fixing” the product, according to a report in Business Insider that cites “three industry sources.”

If true, the question is what does that mean for Square, the company he recently founded to revolutionize the credit card industry?

I emailed both Twitter and Dorsey, and I got the following response (I’ve cleaned up the punctuation and capitalization because that’s how I roll) from Kay Luo, who is now the PR person for Dorsey’s Square:

Jack forwarded me your email. Nothing has changed. He’s CEO of Square and it’s his top priority (frankly, I wouldn’t have joined if this were not the case). He’s also chairman at Twitter.

Note that this isn’t a complete refutation of Business Insider’s story. As Luo points out herself, Dorsey is Twitter’s chairman, so in that role it’s possible that he would consult on product decisions. Clearly he’s not getting too involved in Twitter if he’s still running his own startup, and there’s no reason to believe he’d scale back his involvement in Square.

The more interesting question is whether this reflects tension at Twitter. After all, co-founder Ev Williams took over the CEO spot from Dorsey in 2008, then Dick Costolo took over from Williams in last month. Business Insider reports that Dorsey’s involvement is at Costolo’s request, and that Williams isn’t happy about it.

Twitter did not respond to my request for comment.

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