Diffeomorphic Traces Fail To Detect High-Dimensional Knots
Generalized RBG links and a Plotnick-based construction give counterexamples in every dimension $n \geq 4$, while preserving trace detection for the unknot.
Sep 28, 20264 min2511.07251
Geometric Topology
math.GTManifolds, cell complexes, and geometric structures.
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Alexander Fingerprints Separate Pairs Yet Collide in Databases
Opened-trefoil slots create a binomial determinant coordinate, yielding an $O(n^{-1/2})$ collision bound and a database birthday scale of order $n^{1/4}$.
Sep 10, 20264 min2609.08298