Claytonia whatsis: no, wait, Stellaria probably littoralis
I'm pretty sure that this is a claytonia. It tastes like miner's lettuce, and it has that distinctive growth habit, though the leaves do not wrap around like miner's lettuce leaves do.
Here's what I know about it: it volunteered (I think) in my back yard. I may have planted it -- I certainly planted some claytonia seeds which I thought were miner's lettuce. But several claytonia species which can't really be called miner's lettuce are native to this area. Its details:
Plant is soft from root to flower. Roots are small. Leaves paired. Stems and flowers grow from the leaf joint. Flowers have 5 sepals and ten unfused acute petals. Pistils very small and uncountable at the the top of the ovary. Maybe there are 5 stamens. Ovary and calyx hairy. Ovary has five ovules. Calyx continues to grow after the flower drops, and encloses the ovary loosely while the seeds develop.
What troubles me is that I cannot find a claytonia, or indeed anything in the portulacaceae family, with petals like that. I've seen some provocative flowers -- ones with five petals that are obviously fused from ten -- but nothing with the ten tiny petals.
I did use the dichotomous key in the magnificent huge Jepson Manual of the Higher Plants of California, but as usual I didn't get much of anywhere with it. I was reduced to looking at every page of illustrations, and finally, I just followed my insticts and looked up miner's lettuce to see whether it fit at all. I found the simple pointy leaves for a couple of species. I found a flower that looked more like mine than the others do, but it's on a plant with a thick root and the leaves in a rosette at the soil level instead of trailing all over hell and gone like my plant does. I have, of course, google-imaged claytonia, but with less than satisfactory results.
On a related front, I have discovered that Bacopa, which is a trailing plant which is all the rage in the nurseries, is native to California. But the drawings indicate a much more gracile (and graceful) plant than the nurseries show. Which is the way it goes, in my observations: the dimwits who "improve and select" plants for gardens have a tendency to breed for bigger flowers and more flower-to-plant ratio, resulting in graceless abominations like the garden lupine -- which could be used for a baseball bat with more felicity than as a bedding plant.
ETA: Per the always brilliant Sal Towse, it's not claytonia, but stellaria: I think littoralis though the photo seems to show bigger, flatter flowers and squatter leaves than my guy has. This can easily be explained by the fact that theirs is from Point Reyes and dog knows where mine's from.