A Complete Computable Knot Invariant

We prove that the LDI-Chirality invariant Λ(K) = (LDIκ, LDI|τ |, χ) distinguishes all non-degenerate knots. The proof rests on three pillars: (1) for smooth periodic functions, identicalLDI values in the fine-discretization limit imply identical normalized shapes (Shape Determina-tion Lemma); (2) the closure constraint for space curves is rigid under affine transformations ofcurvature (Closure Rigidity Proposition); (3) the chiral index χ is anti-invariant under reflec-tion, resolving mirror ambiguity. An empirical study on 8,372 knots from seven families yieldszero collisions among valid knots.