Scissors congruence classification in higher dimensions

Determine a complete classification of scissors congruence for polytopes in Euclidean spaces of dimension at least five, extending known classifications in dimensions three (Sydler) and four (Jessen).

Background

The discussion situates the paper within broader developments in combinatorial K-theory, noting parallels with classical scissors congruence problems. Sydler completely classified scissors congruence in three dimensions, and Jessen extended this to four dimensions.

The authors explicitly state that the classification problem "remains an open problem in higher dimensions," highlighting an outstanding challenge in the area closely related to the algebraic and K-theoretic tools discussed.