
Samsung Galaxy Note 10.1
The latest firmware for Samsung Galaxy Note 10.1 (SCH-I925U) is I925UVXAMD1 with Android 4.1.2 (Jelly Bean), released on April 13, 2013 for 1 region (CSC). Every official firmware build for SCH-I925U, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/I925UVXAMD1

SCH-R970X

SCH-L710

SCH-I939D

SCH-I545PP

SCH-I545L

SCH-I435

SCH-I545

SCH-P709
You can find the firmware on the model: SCH-I925U page.
Yes, all firmware files for SCH-I925U are 100% official, original, and obtained directly from Samsung servers.
To flash SCH-I925U, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SCH-I925U.