Rigidity for even and doubly even highly twisted plat diagrams

Let $b$ be a braid word, and consider its even plat closure or doubly even plat closure. For even plats, connect consecutive endpoint pairs at the top and shifted consecutive pairs at the bottom; for doubly even plats, use shifted consecutive pairs at both the top and bottom. Define standard form and highly twisted for these closures analogously to the corresponding notions for plat diagrams. Even and doubly even plat rigidity conjecture. The claims of Theorem hold for such even and doubly even plat diagrams as well. Theorem gives the paper's rigidity and canonical-form conclusions for highly twisted plat diagrams, and this conjecture proposes that the same conclusions extend to the two other natural plat-like closures. The source does not provide evidence that this conjecture has been resolved.