The TARDIS remembers River Song in fragments, scenes like gemstones sifted from history--ordered by heft and size, not time. She breaks the world before she shoots her console, before she is born as a thread knotted within her own walls before she persists for long years in Stormcage prison. Before she saves her Pilot. Before she kills him.
The TARDIS knows every event in discontinuity. Each one is selected, scrutinized for flaws, polished, and set aside. But her expectation, taken over the measure of these events, is wholly unreliable.
Her Pilot follows his own path, tentative but ultimately trusting. Still, the TARDIS' broad-band worry simmers at the edges of their psychic link. Trust is information. Information is the inverse of variance. And to the TARDIS, River Song's impression--stamped across time and her Pilot's shared senses--is patternless.
Synthesize, he tells her. All of her events, summed together. Who is she?
The TARDIS contemplates this. Her Pilot is limited to the single trace of events strung through time and gathered one by one. She is not. She can gather handfuls, if she wishes. If she remembers.
She builds a new perspective. She studies the constants derived from this asymptotic measure, and River Song finally emerges.
When she curbs her psyche to the constraints of space and linear time, the TARDIS learns to remember that her Pilot is in love.