We got word of an imminent update yesterday, and it's here today! Our 2012 flagships should be seeing over the air updates starting today, and the Android 4.4 build has been officially confirmed by Sprint. While a staged rollout will eventually hit your stock, unrooted device, you can force the issue by checking Settings -> More -> About device -> Software update.
Alternatively, the update has been pulled by CNexus over at XDA and can be manually applied. This is the pure, unmodified build, and applying it means a new, KNOX-ridden bootloader and the inability to root at the moment (this will also apply to accepting the OTA). And again, you must be on the latest, MK3 stock build, and take the risk of losing root for good.
Personally, I'm going to wait for a developer to cook up a KNOX-less, pre-rooted version, but if you're ready to take the plunge now, grab the update file here, rename it to update.zip, and move it to your external SD card. From there, boot into your stock recovery (power off, then hold volume up + power + home), and apply the zip.
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Although Samsung had previously confirmed that KitKat would make its way over to the U.S. variants, it's been nothing but quiet on the update front for our two-year-old flagships. However, as of two days ago, the Samsung Open Source Release Center had an inclusion for an L710VPND8 firmware.
Breaking this down, L710 refers to the Sprint Galaxy S3 variant, while ND8 refers to the build number. For comparisons sake, the current firmware version on the S3 is L710VPMK3.
You can check out the discussion thread for the new build over at XDA, and thank senior member poit for tracking down the information. One confirmation we have from CNexus is that the new build will update to the 3.4 Linux kernel, which will bring better battery life, updated sensor drivers, better memory usage, and a host of other backend improvements.
When the update is live, we'll have all of the relevant information for you, so stay tuned.