Empirical Study of the LDI-Chirality Knot Invariant: A Large-Scale Study on 8,372 Knots

We present a comprehensive empirical study of the LDI-Chirality knot invariant Λ(K) =(LDIκ, LDI|τ |, χ) on 8,372 knots from seven families, comprising 35,041,006 pairwise compar-isons. The study employs corrected methodology for Lissajous knots (requiring pairwise co-primality of frequencies) and deterministic seeding for Fourier knots to ensure reproducibility.Results: zero collisions among valid knots, successful discrimination of mutant pairs that defeatclassical polynomial invariants, and correct chirality detection in all tested cases. The invariantcomputes in O(N ) time with N = 10,000 sample points per knot. Complete Wolfram Languagesource code is provided.