UPDATE: Nintendo of America has also confirmed the coming firmware 3DS update. It'll hit on the evening of June 6... which'll be June 7 in Japan. Time zones are real!
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Nintendo updated its Japanese site today with news about the upcoming web browser and eShop update for the 3DS. Originally scheduled as a "late May" update, the new firmware will now hit on June 7... at least in Japan.
That said, it seems reasonable that this will be a worldwide push, since June 7 is also the first day of this year's E3 and the date of Nintendo's pre-E3 press conference, which will take place early that morning. I mean, getting up on stage and saying "And that eShop will let you download all of these amazing new hits (dramatic pause) right now" only works if you don't have to tack "in Japan" onto the end of that sentence. It also only works if you actually have a lineup of amazing new hits to launch along with the eShop.
In addition to the news about the update, which I initially spotted on Andriasang, there's a list of games floating around out there that apparently comes from the latest Famitsu. I haven't seen the magazine for myself, so I won't spend too much time talking about it. Anyway, that supposed list includes a 3DSWare version of the Japan-only DSiWare release, Petit Computer, among other things. So far, the only fully confirmed launch-time release for 3DSWare is Capcom's Mega Man Legends 3: Prototype Version.
While you ponder what this means for 3DS owners around the world, here's a video of a game someone programmed in the DSiWare version of Petit Computer, which looked cooler than I thought it would.