We finally have a 'periodic table' for the microscopic knots that keep your body's proteins from falling apart.
March 20, 2026
Original Paper
Classification of (uncolored) bonded knots and links
arXiv · 2603.18768
The Takeaway
Proteins aren't just floppy chains; they are locked into permanent, complex tangles by internal chemical bridges. This study provides the first systematic classification of these 'bonded knots,' mapping out the foundational architectural library that defines the physical shape of life's most important molecules.
From the abstract
We present a systematic classification of uncolored bonded knots with singularity number at most seven. Bonded knots provide a topological model for closed protein chains with intramolecular bridges, such as disulfide bonds. Following the tradition of knot tabulation, we describe a procedure based on the generation of planar graphs, their conversion into bonded knot diagrams, and the use of the Yamada polynomial together with brute-force Reidemeister moves to distinguish topological knotted type