It is not easy to sort out the taxonomy of this humble weed; we are going by the listing in the USDA PLANTS database, but the species name is also spelled caespitosum (Classical Latin rather than Medieval Latin), and a whole group of related Polygonum species is often separated into the genus Persicaria, in which case this becomes Persicaria posumbu. It is one of several similar smartweeds that frequently pop up in urban areas. This one is distinguished by its dense spike of tiny pink flowers and pointed leaves without markings; the similar Lady’s Thumb (Polygonum persicaria or Persicaria maculosa) has a dark thumbprint mark on each leaf. Look also for tufts of hairs at the stem joints. These plants were growing by a fence in Beechview, where they were blooming in the middle of July.
Gray describes the genus Polygonum and the section Persicaria. He does not describe this species, because it seems to be a twentieth-century introduction; but the description we have given above should distinguish it from the other members of its genus that grow around here.
POLYGONUM [Tourn ] L. KNOTWEED. Calyx 4-6 (mostly 6)-parted; the divisions often petal-like, all erect in fruit, withering or persistent. Stamens 3-9. Styles or stigmas 2 or 3; achene accordingly lenticular or 3-angular. Embryo placed in a groove on the outside of the albumen and curved halfway around it; the radicle and usually the cotyledons slender. Pedicels jointed. — Ours all herbaceous, with fibrous roots (except in P. viviparum), flowering through late summer and early autumn. (Name composed of poly-, many, and gony, knee, from the numerous joints.)
PERSICARIA [Tourn.] L. Flowers in dense spikes, with small scarious bracts; leaves not jointed on the petiole; sheaths cylindrical, truncate, entire, naked or ciliate-fringed or margined; calyx colored, 6-parted, oppressed to the fruit; stamens 4-8; filaments filiform; cotyledons accumbent.