Abstract : Using validated numerical methods, interval arithmetic and Taylor models, we propose a certified corrector-predictor loop for tracking zeros of polynomial systems with a parameter. We provide a Rust implementation and benchmark it against HomotopyContinuation.jl, a state-of-the-art uncertified homotopy continuation implementation. Finally, we briefly present an effective approach for decomposing geometric braids induced by root continuations in terms of Artin’s braid
group presentation, using certified path tracking (ongoing work).