shortbeak arrowhead, Sagittaria brevirostra

These plants along Black Creek got my attention because they were so enthusiastic. The inflorescences were the largest I've seen with arrowheads; branched and very many flowered. Could they be something different? Shortbeak has longer beaks on the seeds than its closest relative, and they mostly point in a different direction. You have to take some home and magnify and carefully measure. And then you still might not know. These beaks qualify. The rest of the plant, not as much. The pros at M (go Blue!) lean toward a different identification. And shortbeak is extremely rare here. But for the sake of argument and another image, here it is. Shortbeak arrowheads are found in CA, CO, IA, IL, IN, KS, KY, LA, MD, MI (not collected here for sure since 1861), MN, MO, MS, ND, NE, NM, OH, OK, SD, TN, TX, VA, WI, NB, and SK. Lenawee Co MI, 9/4/16. Water-plantain family, Alismataceae.