Kyty
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Check here for downloaded early stage emulator
Kyty is a PS4 & PS5 emulator in the very early stage, but looks quite promising. While the graphics for PS5 are not yet implemented, it's possible to run some simple PS4 games, but don't be surprised if they also have graphical glitches, crashes, freezes and low FPS. All in all, it's still being actively...
Spine
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Spine's Wine-like PS4 emulator for Linux ONLY is capable of playing some basic commercial games, albert with usual early in development limited performance and accuracy. That said, Flatpak instructions is available on Github or you can download latest release from here (dated 01/09/2021).
It's still very actively developed and seems promising.
PS4Delta
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PS4Delta is a very high level PlayStation 4 emulator, written in c++. It's quite early in the development stage and barely manages to initialize all firmware modules though is actively being worked on.
Relevant Files
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PS4 Firmwares
fpPS4
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fpPS4 is a PS4 emulator for Windows and more specifically a “PS4 compatibility layer over Free Pascal”. According to the developer, this project is made for fun and is still in its infancy.
It's already capable of running some commercial games such as Sonic Mania as these particular type of games are often used for early testing. It's due to them using less advanced function calls and possibly less 3D which makes them easier to be a starting point.