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
CWDWEWF♯HGWAWBHC
What is true of it
C Lydian is C, D, E, F♯, G, A and B, and back to C.
Its steps are W – W – W – H – W – W – H, where W is a whole step and H a half.
On the same tonic, C 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
CmajorCmaj7major seventhDmajorD7dominant seventhEmminorEm7minor seventhF♯dimdiminishedF♯m7♭5half-diminished seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.