Every Plat Presentation Admits a Positive Bounded Braid Representative

What the math gives to ML

The paper supplies an explicit algebraic normalization mechanism for braid presentations: Garside left-greedy normal form separates a braid into a power of the fundamental element and positive simple factors, while the inclusion \(\Delta\in H_{2n}\) permits removal of that power without changing the Hilden double coset. This is transferable as a structure-preserving tokenizer and canonicalization layer for models operating on braid words, link presentations, or other quotient-structured symbolic data. The strongest practical use is replacing long, non-unique generator strings with positive Garside-factor sequences and training with equivalent representatives mapped to the same normalized form.