Exact Chained-Word Threshold and Monotone-Path Structure in the Even Root-of-Unity Kaleidoscope Yang-Baxter Algebra

Qihang Wang, Zhiyuan Yao

Qiu, Guan, and Yu conjectured that in the even-order Kaleidoscope Yang--Baxter equation every word $\Lambda T^{k_1}\Lambda \cdots T^{k_M}\Lambda$, built from a square-zero matrix $\Lambda$ and integer power…