By the power of truth, I, while living, have conquered the universe.
Cortana was created November 7th, 2549. Given that smart AIs go rampant after 7 years, she'd have descended into rampancy by 2556 (as CIA391 kindly points out).
The Dawn is still adrift by 2559, Halo Legends: Origins depicts her now pretty much fully rampant; her form switches between red and purple, and we see the IRIS Glyph in her eye 9what this means, we do not know yet).