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It's started by 1:40 AM (IST) on 04th July, 2013 and still it showing down.
To be double assured I checked it at downforeveryoneorjustme.com too, below is screenshot which confirms it's down.
So you all Tweeple who are clueless of what's went wrong don't worry. It's something wrong from their end. Between I just browsed through Official Twitter Status http://status.twitter.com/post/52079734757/twitter-site-issue and they had confirmed - "Some users may be experiencing issues accessing Twitter. Our engineers are currently working to resolve the issue."