
Samsung GALAXY CORE
The latest firmware for Samsung GALAXY CORE (SHW-M585D) is M585DKXU0AOH1 with Android 4.1.2 (Jelly Bean), released on August 18, 2015 for 1 region (CSC). Every official firmware build for SHW-M585D, 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/M585DKXU0AOH1

SHW-M486W

SHW-M580D

SHW-M570S

SHW-M500W

SHW-M480W

SHW-M480S

SHW-M440S
You can find the firmware on the model: SHW-M585D page.
Yes, all firmware files for SHW-M585D are 100% official, original, and obtained directly from Samsung servers.
To flash SHW-M585D, 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 SHW-M585D.