To understand why you can’t downgrade to iOS 6, we need to look at the iOS update and restore processes. Basically, after you install a new version of iOS — either over-the-air on your device, or via an IPSW file in iTunes — your device phones home to Apple. Apple then checks to see whether the newly installed version of iOS is signed — as in, the cryptographic signature of the files matches a list of approved signatures on Apple’s servers. This serves three purposes: First, it makes sure that none of your files are corrupted or infected with malware; second, it ensures that you’re only running an approved version of iOS; and third, there’s the small point of fragmentation. One of the strongest features of Apple’s mobile ecosystem is that every device runs the same operating system. If users could downgrade freely, then the story might be very different.
Basically, during the grace period, Apple’s servers still accept the signature of previous versions of iOS (iOS 6.1.3 and 6.1.4 in this case) — and then, when that period ends, only the latest version is accepted (iOS 7). If your version of iOS doesn’t match Apple’s approved list, your device will refuse to work until you reinstall an approved version (iOS 7 in this case). This is why you will read some reports of people being able to downgrade from iOS 7 to iOS 6, but why none of the guides you find online will work.
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