Combinatorial invariance of Kazhdan–Lusztig polynomials
What the paper claims, in its own words
Resolves the full combinatorial invariance conjecture: isomorphic Bruhat intervals in arbitrary Coxeter systems have identical equal-parameter Kazhdan–Lusztig polynomials. Thus the abstract order of the interval determines the polynomial, even across different Coxeter systems.
The plain-language explainer for this entry is still coming.