Is P0^{EQ} equal to Γ2?

Determine whether the class of problems computable by constant-cost deterministic protocols with oracle access to Equality (P0^{EQ}) is exactly the class of problems with constant γ2-norm (Γ2); i.e., prove or refute P0^{EQ} = Γ2.

Background

Prior work showed P^{EQ} ⊆ Γ2 and explored the tightness of this inclusion. The authors reiterate this as one of the central open problems in the area, tied to the geometric factorization norm γ2 and Equality-oracle computation.

A resolution would settle whether Equality-oracle protocols capture precisely the γ2-behavior of matrices, bridging combinatorial and geometric perspectives in communication complexity.