Recently Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the connective constant of self-avoiding walks on the honeycomb lattice is √ 2 + √ 2. A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) model with n ∈ [−2,2]. We modify this model by restricting to a half-plane and introducing a fugacity associat...