hello, tipularia looks like a Chamaesyce, most likely C. maculata. widely distributed in Japan since being introduced from North America in 1887.
Eeeks!!! It looks very similar to purslane, aka portulaca olcea. My daughter once brought a few of these plants over to show me that she had purchased. It must have dropped some seeds and took off over the years. It has become to invasive that I have to weed and weed trying to get it out of all my gardens. I do not compost this ever, but it still persists. I don't know if it is purslane, but yikes!!!! If it is, I can see why you call it a doily because it is inded so flat, and so STRONG!!!
Very good pedalada! So, it has invaded Japan. It might be on every continent by now. Spotted Sandmat, Chamaesyce maculata It used to be Euphorbia maculata. A closeup of the flowers would have given it away as a Euphorbiaceae. Be careful if you handle it. It can cause contact dermatitis. It does look similiar to Portulaca oleracea from a distance.
The scorch of my lawn, and stubborn inhabitors of the cracks in my drive way. Dandelions, at least, will "reward" me with cheery yellow flowers. This thing is a weed through and through.
