The fibered-knot coefficient conjecture for theta
Let be a fibered knot, and let be the degree of its Alexander polynomial , meaning the highest power of . Consider the coefficient of in , which is a polynomial in .
Fibered-knot coefficient conjecture. This coefficient is an integer multiple of
The claim would provide a fast-to-compute fiberedness criterion and can be stronger than the Alexander condition. The authors state that they have no theoretical support for it, so it remains open.
References
Primary source
Dror Bar-Natan and Roland van der Veen, “A Fast, Strong, Topologically Meaningful and Fun Knot Invariant”, arXiv:2509.18456 (2026).
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