Unique representation of n-point MHV gravity amplitudes

Establish the unique representation of the n-point maximally helicity-violating (MHV) gravity amplitude as formulated as a commutative algebra problem in Koefler–Oktem–Paranjape–Trnka–Zacovic (Conjecture 2.1).

Background

MHV gravity amplitudes admit conjectural uniqueness characterizations via interpolation-like constraints on flag varieties and related commutative algebra descriptions. Proving uniqueness would bridge geometric interpolation conditions with amplitude numerators, informing both the structure of canonical forms and potential positive-geometry interpretations for gravity amplitudes.