Real ETF positivity-or-negativity conjecture

Let $D$ and $N$ be positive integers with $N>2D>2$, and let a real $\operatorname{ETF}(D,N)$ denote a real equiangular tight frame of $N$ vectors in dimension $D$. Call $(D,N)$ positive or negative when it satisfies the positive or negative conditions defined in the source. Real ETF positivity-or-negativity conjecture. If a real $\operatorname{ETF}(D,N)$ exists, then $(D,N)$ is positive or negative. The conjecture is motivated by the fact that every known real ETF in this range is positive or negative, but the cited nonexistence examples show that the relevant necessary conditions are not sufficient in general; the conjecture remains open.