The mim-width hardness conjecture for NP-hard distance (σ,ρ)(\sigma,\rho)(σ,ρ) problems
Mim-width hardness conjecture. Every \NP\NP\NP-hard distance (σ,ρ)(\sigma,\rho)(σ,ρ) problem is \W[1]\W[1]\W[1]-hard when parameterized by mim-width.