Let’s talk about why you specifically want the 4K version, not a 1080p re-encode.
The name "4K77" refers to the project's technical specifications: a scan of a film released in 1977 . Unlike other fan efforts that "despecialize" the movie by digitally editing modern Blu-ray footage (such as Harmy's Despecialized Edition ), 4K77 is a direct digitization of original 35mm film prints.
Head to Archive.org, search "Project 4K77 1.4," and prepare to see a galaxy far, far away as it truly was—beautifully flawed, gloriously grainy, and deeply human.
How was it found? Through a network of film collectors, archivists, and what some would call “film detectives.” A print was located in the hands of a private collector in the UK. After negotiations (and, reportedly, a small financial compensation to the owner), the print was loaned to Team Negative 1.