No Non-Empty Odd Independent Set Exists in the Infinite Queen Graph

We prove that the infinite queen graph on ℤ² admits no non-empty odd independent set. In particular, it admits no infinite odd independent set. The argument is algebraic: we encode rows, columns, diagonals, and anti-diagonals by 𝔽2-valued indicator functions, derive two recurrence relations, force a collection of queen-lines to be bad, and then obtain a contradiction from parity at four carefully chosen lattice points. Thus the open problem posed for the infinite Queen graph in Caro, Petrusevski, Skrekovski, and Tuza, in the stronger form considered here, is completely resolved.