Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
FWGWAWBHCWDWEHF
What is true of it
F Lydian is F, G, A, B, C, D and E, and back to F.
Its steps are W – W – W – H – W – W – H, where W is a whole step and H a half.
It uses no sharps and no flats at all: seven letters, seven white keys.
On the same tonic, F major differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 32 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
Found by testing every chord in the catalogue against these 7 sounds, not chosen.