Uniform folded ribbonlength conjecture for (2,q)-torus links

Let T(2,q)T(2,q) denote a (2,q)(2,q)-torus link, let [T(2,q)][T(2,q)] denote its link type, and let Rib([T(2,q)]){\operatorname{Rib}}([T(2,q)]) denote its infimal folded ribbonlength. Uniform torus-link conjecture. There is a constant C>0C>0 such that

Rib([T(2,q)]){q+3when q10,8313.86when q11 is odd,Cwhen q12 is even.{\operatorname{Rib}}([T(2,q)])\leq \begin{cases} q+3 & \text{when }q\leq 10,\\ 8\sqrt{3}\leq 13.86 & \text{when }q\geq 11\text{ is odd},\\ C & \text{when }q\geq 12\text{ is even}. \end{cases}

The statement combines explicit small-crossing bounds with uniform bounds for the odd and even families; the paper presents it as a conjecture following constructions and previously known uniform estimates.

Sources & referencesView supporting material

Primary source

Zhicheng Chen, Elizabeth Denne, Kyle Patterson and Timi Patterson, “Ribbonlength upper bounds for small crossing knots and links”, arXiv:2510.16190 (2025).

Additional references

2 papers in this index state this conjecture (2025). The statement above is taken from the most recent of them; the others are arXiv:2509.18370.

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.