Last time I found a paper in Graphics Gems titled Solving the Nearest-Point-on-Curve Problem, which transforms the problem into a Bernstein polynomial form. Then an exact solution can be obtained using A Bézier Curve-Based Root-Finder. This is my implementation [1], but it's not very robust for high-degree cases.
This was my first instinct as well, which makes sure numbers are adjacent. OP also mentioned this variant as lucidBrot/hexgridspiral in the older post.
This is a feature of arxiv that automatically converts text looks like a link into "this http url". The submitter missed the space after the "." in "...strong reasoning ability. OpenAI has claimed...".
A funny game!
For anyone else struggling with the wordle, the answer is here[1].
For anyone else struggling with the country, you can fill in the names of all the countries, then run a bisection.