 The analogous relation for classical logic would be universally representative (and thus not special), at least in any fragment which, as well as having →, has either ⊥ or ∧, since any φ and ψ are here respectively equivalent to (φ → ⊥) → ⊥ and (ψ → ⊥) → ⊥, where they are linked explicitly by having a common χ at the head of the main implication. (Alternatively with ∧, replace ⊥ here by φ ∧ ψ.) But in the intuitionistic case the relation of being head-linked is special since, for example, with Peirce’s law σ(p,q) = (p → q) → p ≻ p, we have σ(p, q) intuitionistically unprovable but we have σ(φ,ψ) ∈ ⊢I L for any head-linked  φ, ψ.