It's not really a fake river boundary because for a very short segment (maybe a mile) the state boundary actually happens to follow a river, but the US 64 bridge at Fort Smith crosses over from Arkansas into Oklahoma at that location.
I never noticed that. According to the USGS map, the state line follows a (roughly) straight line up to Mill Creek, and then follows Mill Creek a few hundred feet to the Poteau River. It then follows the Poteau River about 1.6 miles to the Arkansas, just south of US 64. It follows the Arkansas River 0.4 mile and splits off just north of US 64.
Mill Creek starts in a hollow dividing George and Brooks Stephins Mountains, just south of I-540. It's about 7.5 miles long and its drainage area is quite narrow, with areas to the west draining into the Poteau and to the east draining into the Arkansas below Fort Smith. That makes me wonder whether this is the most minor stream that carries a state line.
I just lost 30 minutes of my day looking more into the OK/AR boundary, and it was interesting enough I figured I had to post about it here. It is a fascinating mess of legal documents, treaties, and bad surveys. The Arkansas State Constitution defines the state boundaries, but does not explicitly define the western boundary, leaving that to acts of Congress and treaties existing at the time of statehood. But the act of Congress that admitted Arkansas to the US also does not explicitly define the western boundary, instead referencing the 1828 Treaty of Washington between the United States and the Cherokees:
The Western boundary of Arkansas shall be, and the same is, hereby defined, viz: A line shall be run, commencing on Red River, at the point where the Eastern Choctaw line strikes said River, and run due North with said line to the River Arkansas, thence in a direct line to the South West corner of Missouri.
So that only defined the half north of the Arkansas River, and even that depended on the eastern boundary of the Choctaw Nation - which had been contentious ever since the beginning. The original 1820 treaty with the Choctaws put that line between the Arkansas and Red Rivers roughly between Morrilton and Fulton, AR. But white settlement had already advanced past there, and Congress tried to move the boundary to 40 miles west of the southwest corner of Missouri. A compromise line was set in an 1825 treaty:
a line beginning on the Arkansas, one hundred paces east of Fort Smith, and running thence, due south, to Red river
A surveyor named James Conway was selected to survey that line, but he did not survey it directly to the south probably under intense pressure from the white Arkansas settlers. The Conway line angles slightly southwest, but the US government did not acknowledge this until the 1870s when the Choctaw were compensated for the bad survey.
After that the boundary was set at the Conway line, but that created a small strip of Choctaw land east of the Poteau River (and Mill Creek) where laws were rarely enforced. The Arkansas district court got jurisdiction over the strip to deal with that, and then Arkansas began to collect taxes from businesses there. Arkansas finally asked Congress to just make it part of Arkansas, which was done in 1905. The new legal definition in the Fort Smith area became:
Beginning at a point on the south bank of the Arkansas River one hundred paces east of old Fort Smith, where the western boundary line of the State of Arkansas crosses the said river, and running southwesterly along the south bank of the Arkansas River to the mouth of the Poteau; thence at right angles with the Poteau River to the center of the current of said river; thence southerly up the middle of the current of the Poteau River (except where the Arkansas State line intersects the Poteau River) to a point in the middle of the current of the Poteau River opposite the mouth of Mill Creek, and where it is intersected by the middle of the current of Mill Creek; thence up the middle of Mill Creek to the Arkansas State line; thence northerly along the Arkansas State line to the point of beginning
Interestingly, in 1985 Oklahoma actually sued Arkansas for control over that strip of land. They lost.