The kernel source was posted just the other day, which usually signals an update is right around the corner. Indeed, here comes KitKat for the Galaxy Note 3 on Sprint. The 503.6MB OTA download includes a few small tweaks to TouchWiz with Android 4.4.
Here's the changelog for the OTA, version number N900PVPUCNAB.
- Android 4.4
- Music album art on the lock screen
- Launcher selection in settings
- Camera shortcut on lock screen
- Improved user interface and stability
- Prevention pop-up removal
There may also be some Sprint-specific bits in the update, but most of the changes are directly related to KitKat. The OTA is popping up in a lot of places, so you might to be able to trigger the download by checking for updates in the system settings. Otherwise, it will invade your status bar at some point in the next few days.