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on Tight alternating knot constant ($C_{22b}$)

The statement

$C_{22b} = b_{o}$ is the largest constant for which one has an inequality

L \geq b_{o} C

for all knots that admit an alternating diagram, where $L$ is the ropelength of a knot (or link) with crossing number $C$ . The ropelength $L$ is the infimum over all embeddings of the knot (or link) of the ratio of the contour length of the knot to its thickness. The thickness is defined as the radius of the smallest circle that passes through any three points on the knot (where collinear points yield an infinite radius). Colloquially, the ropelength is the least amount of rope required to tie a specific knot in a rope of unit radius. See [CKS2002] for the full definition.

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.