Do You Weed Me?

This is the weed that has completely dominated the Whitewater garden since it became ours. I've battled the monster for four years, but it still keeps coming back, strong as ever. There must be trillions of eternally viable seeds in what otherwise would be great garden soil. Can anyone help me identify it? (The stuff surounding it is purslane, I know, and I can deal with that, or even eat it.)

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And here is a smart looking asparagus patch—circular in orientation, and manageable. Since aspergrass migrates, a circle is a good idea, it seems to me. Once the center is vacated, it can be re-fertilized and re-planted, and then it's concentric.

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"Even if I knew tomorrow the world would go to pieces, I would still plant my apple tree."
                                           —Martin Luther