Nonexistence of almost-complete Harary polynomials

Let $\mathbb{G}(n,1/2)$ be the random graph model with edge probability $1/2$, and let a Harary polynomial be a graph polynomial arising from a graph property. A graph polynomial is almost complete when asymptotically almost all graphs in the model are uniquely determined by it.

Harary almost-completeness conjecture. There is no Harary polynomial which is almost complete for $\mathbb{G}(n,1/2)$.

This is proposed in contrast with the Bollobás–Pebody–Riordan conjecture for the chromatic polynomial. The supplied text gives no resolution or supporting theorem for this stronger nonexistence claim.