Positivity conjecture for the massless time-like XX-chain correlation

Consider the massless time-like regime of the XX chain and the complex correlation function $(-1)^m\langle\sigma^-_1(0)\sigma^+_{m+1}(t)\rangle$. Positivity conjecture. Both its real and imaginary parts remain positive in the massless time-like regime. The statement is presented as an experimental proposal concerning the sign of the numerically evaluated correlation function; no proof or resolution is supplied.