θ-invariant cardinality bound for Urysohn spaces with an H-closed π-base

Establish whether the cardinality bound |X| ≤ 2^{wL(X) t_θ(X) ψ_θ(X)} holds for every Urysohn Hausdorff space X that admits a π-base whose elements have H-closed closures, where t_θ(X) is the θ-tightness and ψ_θ(X) is the θ-pseudocharacter of X.

Background

After introducing θ-variants of cardinal invariants (θ-density, θ-tightness, θ-pseudocharacter) for Urysohn spaces, the authors observe that ψ_θ(X) ≤ k(X). This motivates their explicit question of whether a cardinality bound involving θ-tightness and θ-pseudocharacter, analogous to previously established bounds, holds universally for Urysohn spaces with an H-closed π-base.