Reversal-symmetry conjecture for multilinear period 1 polynomials

Let $P=P(x_1,\ldots,x_n)$ be a multilinear polynomial with positive coefficients that generates a period $1$ seed. Reversal-symmetry conjecture.

$$P(x_1,x_2,\ldots,x_n)=P(x_n,x_{n-1},\ldots,x_1).$$

This predicts reversal symmetry for all such multilinear polynomials. The paper presents it as an unproved conjecture, alongside further proposed classifications of positive period $1$ polynomials.