Local Divergence Intensity as a Knot Discriminator: Empirical Results on 259 Knots with Zero False Collisions

We present empirical results demonstrating that Local Divergence Intensity (LDI), com-puted from discretized curvature and torsion sequences of space curves, successfully discrim-inates 259 distinct knot types with zero collisions between topologically distinct knots. Thetest library spans torus knots, Lissajous knots, twist knots, and standard tabulated knotswith crossing numbers from 3 to 100. The minimum distance observed between distinctknot types was 8.12 × 10−4 , occurring between two Lissajous knots L(3,5,16) and L(4,5,17).These results substantially exceed the discrimination capacity of classical polynomial in-variants, which exhibit their first collisions at 6–11 crossings. We describe the digitizationmethodology in detail, enabling reproducibility.