Inequivalence conjecture for rooted spanning trees and initial states in de Bruijn sequence generation

Let $F_h$ be the feedback function defined from a nonsingular function $h$ in Equation, with $n\geq m+2$. An input pair consists of a rooted spanning tree and an initial state, and two input pairs are distinct when either component differs. Inequivalence conjecture. Distinct input pairs generate inequivalent de Bruijn sequences of order $n$ under both the GPO and GJPO algorithms. This conjecture is motivated by computational evidence; its general validity for the stated feedback functions and parameter range remains open.