The Meaning of Clara Oswin Oswald

Clara: clear, bright, famous
Oswin: God's friend
Oswald: God's power

Within hours of The Snowmen (nah, hours of Asylum), theories of Oswin's true identity began to circle the web. Some of the simpler ones suggest she's an already-existing character, such as Romana, the Rani, Susan, Jennny, or Donna. She could also be a child of canon characters, such as River/Doctor, Rose/Meta-crisis, or Jenny/Jack.
What suggestions do we have that might hint at her identity?

Her "absolutely true" bedtime stories:
 Invented fish to go swimming with her
 random association: Jim the Fish, fish that can swim in fog, Colin the goldfish, the Atlantian fish-people, starwhales

Born behind the face of Big Ben, accounting for her acute sense of time.
random association: Rose and Jack danced at Big Ben during WWII, the pig-alien's ship destroyed Big Ben during aliens of London,  could be a reference to TARDIS-conception

There is obviously some connection beyond mere resemblance for Oswin and Clara. Both mentioned a passion for souffles, as well as the same personality. But the real clincher is her last words, both times.

Run, you clever boy. And remember.

Remember what? AGH! MOFFAT! First, we met Oswin in the future. Then Clara in the past, and  (presumably), another version of her from our time period.

One of the cleverer theories I've seen is that Clara is a repetitive message, much like "Hello Sweetie" or "Bad Wolf," but more complex. To quote

Let's just say someone/something is trying to send the Doctor a message. Could be a warning, a distress signal, a bait, whatever. But contacting the Doctor can be fiendishly difficult, as ''The Pandorica Opens'' already demonstrated - and *that* was by the Doctor's own personal friends.Furthermore, the 'one word test' in ''The Snowmen'' can be seen as a discussion of the limitations of language. Sometimes a topic arises is complicated enough that, no matter how smart or witty you are, you can't summarise it with one word. Sometimes you need to clarify, demonstrate, answer questions, etc.So instead of a page of paper, or a holorecording, or something so limited, a message is coded in the form of a pattern throughout history. A sentient pattern, capable of certain behaviours that attract the attention of the recipient. A pattern that stores a virtually uncountable number of words in its vocabulary, and can flexibly adapt their usage to suit the situation. A pattern that is a person...

Intriguing, but it doesn't quite seem to fit for me. The word that kept coming up when I considered Clara was "echoes" or "projection." In the actress's first appearance, she projected a human voice while trapped in the form of a Dalek. Perhaps that's a hint to her true identity.

My Theory
I'd kind of like Clara to be the Doctor and River's child--I mean, who knows how their genetics would combine--but that makes the kiss extremely awkward. Instead, I think Clara is a "projection" of River Song, post-Library. The library has holographic and replication technology--like the Node--and with access to so much information, constructing bodies seems possible.
It also seems to fit, personality-wise. Both River and Clara are flirty, straightforward, and adventurous ladies, who aren't afraid to tease the Doctor.  Yes, there are a few differences, but she seems to have a similar "essence" to River Song. It would also explain Clara's serendipitous use of the word "pond" when subjected to the one-word test. Not to mention their final words.

You and me. Time and space. You watch us run.

River Song,  "Forest of the Dead."

 Run, you clever boy. And remember.

Oswin Oswald, "Asylum of the Daleks."
Clara Oswin, "The Snowmen."

Another aspect that seems to seal the deal for me is her reference to being born "behind the face of Big Ben," accounting for her "acute sense of timing." It doesn't take too many associations to connect this joke with River's conception in the Time Vortex.  As part Time Lord, she certainly has an "acute sense of timing," down to always being caught by the Doctor when she jumps off things.