Should I be fighting this as a noxious weed, or is it OK to live with it?  It currently is a single plant, just showed up this year.  It's about 5' tall.

Hi Tina,

You are correct that this is not Japanese knotweed (Fallopia japonica), Giant knotweed (F. sachalinensis), and their hybrid, Bohemian knotweed (F.x bohemica) all List A Noxious weeds in Colorado. 

https://ag.colorado.gov/conservation/noxious-weeds/species-id

I do think that this may be Persicaria lapathifolia (also Polygonum lapathifolium or Persicaria lapathifolia) also referred to as curlytop knotweed, pale smartweed, and dock leaved smartweed among others.  It is not included in the noxious weeds of Colorado, however, it is a quite common weed across the US.  Behaviorally, it does spread quite easily along waterways and can cause issues in irrigation ditches when allowed to spread uncontrolled.  The seed heads are plentiful.  The whole plant can be removed before seed distribution to control spread.

http://ipm.ucanr.edu/PMG/WEEDS/pale_smartweed.html

https://wric.ucdavis.edu/information/natural%20areas/wr_P/Polygonum_lapathifolium-persicaria.pdf

Hope this helps.

Sincerely,

Boulder County Master Gardeners