I would ditch that compost pile and start over. Don't take any chances. Seriously, it's that bad. Here's the thing: as long as your neighbor is married to the idea of keeping the plant, you are fighting a losing battle. Might I suggest that you find a website with info on it, print it off, and have a friendly chat with your neighbor? If he attacks the mother plants, you have a better shot with yours. This is the battle plan: two or three times during the growing season, cut it back. Then around July let it grow. When it gets nice and thick in August, cut it down to a short stub and paint the stub with concentrated Roundup, either straight up or diluted 1:1 with water. In the late summer or fall, the plant's vascular system is drawing energy down to the roots to prepare for winter, so the chemical is more effective at that time. If it resprouts that fall, do the same again. Then in spring, spray any new shoots early with regular diluted Roundup (only use the concentrate if you are painting and/or injecting stems; never spray full-strength concentrate Roundup). Once again keep it contained next summer by cutting it down a few times and cut and paint again in the fall. If any new growth starts in a brand new location, spray it while it's small. Then next fall, cut and paint again. However, this will only succeed if your neighbor agrees to attack Momma Knotweed. Otherwise, the rhizomes will keep spreading over to your yard. Maybe you can sweeten the deal by offering to replace the plant (when it is well and truly dead) with a less invasive screening plant? I guess it all depends on how well you get on with your neighbor. By using this method, we have reduced our knotweed by maybe 50% over two-and-a-half years, and that includes areas where we were not very diligent because we ran out of time. If you just try to pluck it out of the ground, it will grow forever. This is not a rhizome that you will exhaust with manual removal alone. Here's a link: http://www.skamaniacounty.org/Noxious_Weeds/TNCreport.htm I suggest bringing that to your neighbor, if your relationship is good enough.

No! No! No! It's not done by squirrels or rabbits or groundhogs. It's a weevil (the "Sunflower Head-Clipping Weevil). I removed the one below from my purple coneflower and brought it in the house for a picture. I also killed 20 of his friends. What you have to do is walk around your garden and when you see a flower deadheaded 2 inches from the top, put your hand (or cup) underneath the flower and squeeze. These weevils will fall out into your hand or cup, and you can kill them with prejudice. They don't bite. :) You will also see them on top of the flowers and sometimes crawling up the stem. I've manually removed them every few days, and the problem is mostly resolved. I also found more details just now at: https://bygl.osu.edu/node/816 Good luck!

Just as a comment, perhaps relevant, perhaps not... I've been growing Dalea purpurea for some years now from seeds originally purchased from a restoration company up in Edmonton. This summer, my route to work has been through Bowmont Natural Environment Park, where I've, for the first time, noticed purple prairie clover in the wild. (Yeah, not too observant, I know, but anyway...) The ones I grow at home are in horrible, unimproved clay along the fence, and any "topsoil" (a euphemistic term around here for clay with most of the rocks screened out) that may once have been there, was probably largely removed when we dug out the turf. The only benefit they get is watering from a soaker hose along the back of the bed near the fence, if there's been no rain for some time. Compared to those I've seen this summer in an essentially "wild" setting (no mowing, no watering, no grazing), the ones at home are much larger, lusher plants. They are 2 to 4 times taller, have many more stalks per plant (about 3 on a quite robust specimen in the park, versus more than 10 and even well over 20 on my plants). The stems are also very leafy at home, while the others are very sparse. The flower heads on those in the park are compact wide little cylinders (up to ~2 cm long), while those at home are narrower, elongated wands up to 7 cm long (av. ~ 4-5cm). There is competition, too, from other plants at home, though I can't judge how it compares to that in the park. So, even in what I think of as really crummy gardening conditions (typical of Calgary, sigh...), it seems life is a lot easier for them than in Bowmont Park...I found it surprising that the difference was so large.

Definitely not Society Garlic. The blooms are much smaller than those of Dietes. The blooms are about 1" diameter, star-like, individual (not a tight cluster) at the end of short stems (3-4", approx) attached to the top of taller stems rising from the base of the plant. It's in a residential neighborhood, at the edge of the sidewalk facing west. It would likely get plenty of sun exposure after noon. I've considered taking my phone to get a photo, but I want to be free from my phone during my morning walk. The neighborhood is peaceful and quiet with pretty gardens. Carrying even a small camera on a 3-4 mile walk would be a nuisance to me.