
Samsung Galaxy Tab4 10.0
The latest firmware for Samsung Galaxy Tab4 10.0 (SM-T531) is T531XXS1BRH3 with Android 5.0.2 (Lollipop), released on August 16, 2018 for 4 regions (CSC). Every official firmware build for SM-T531, 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/T531XXS1BRH3
SM-T531 started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.0.2 (Lollipop). The newest build, T531XXS1BRH3, was released on August 16, 2018. No new build has appeared for 99 months, so regular updates for this model have most likely ended.
Box codes of SM-T531 for different colors and markets. Firmware is chosen by the model code SM-T531 and your region (CSC), not by the SKU.

SM-T537A

SM-T530X

SM-T535

SM-T532

SM-T638B
The newest firmware for SM-T531 runs Android 5.0.2 (Lollipop): build T531XXS1BRH3, released on August 16, 2018.
The latest build for SM-T531, T531XXS1BRH3, was released on August 16, 2018 (8 years ago).
SM-T531 has had no new firmware for 99 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T531 are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T531, 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 SM-T531.