I think I found tethered jailbreak for iPhone 4 on iOS 7.0.3
Submitted by Jessica Brown on Wednesday, October 23, 2013.
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Hi. There is a video that shows someone running Cydia on an iPhone 4 running iOS 7.0.3. However, I am not sure, but I think it only works on iPhone 4. Also, the jailbreak is tethered and only works on mac, not windows. It is just a script, not a jailbreak computer program, so it is harder to do. You can't just hook up your phone to your computer and hit the jailbreak button. However, I think the page for the video also has a link to the script and a link to a written guide on how to jailbreak 7.0.3. Here's the link to the video. Good luck if you try it. m.youtube.com/watch?v=nF43aCTSw1c&feature=youtu.be&desktop_uri=%2Fwatch%3Fv%3DnF43aCTSw1c%26feature%3Dyoutu.be
Call me a skeptic ... but really?