It looks likely 7.51 and probably up to 7.55 will be able to run homebrew in the next month or two also thanks to a publicly disclosed kernel exploit that seems to have been patched in 8.00. The specific kernel exploit has already been implemented and successful on FreeBSD so it's likely only a matter of time before it gets ported over to 7.55 PS4. Today though 7.02 is the latest exploited firmware.