Conjectured two-point correlations for the type B MultiTASEP

Let $n$ be the rank parameter of the type $B$ MultiTASEP, and write $\langle a,b\rangle$ for the two-point correlation of entries in the last two positions, with barred symbols denoting signed entries. The preceding text gives the identity $\langle i,\overline{j}\rangle=\langle i,j\rangle$. Conjectured two-point correlations. For the last two positions in the type $B$ MultiTASEP, the following identities hold:

$$\langle \overline{i},\overline{j}\rangle=\frac{1}{(2n)^2}\quad (3\leq i\leq n,\ 1\leq j\leq i-2),$$ $$\langle \overline{j+1},\overline{j}\rangle=\frac{1}{(2n)^2}+\frac{n^2-j^2}{4n^2(2n-1)}\quad (1\leq j\leq n-1),$$ $$\langle \overline{i},\overline{j}\rangle=\frac{j-i}{2n^2(2n-1)}\quad (1\leq i\leq n-1,\ i+1\leq j\leq n),$$ $$\langle i,\overline{j}\rangle=\frac{i+j-1}{2n^2(2n-1)}\quad (1\leq i\leq n-2,\ i+2\leq j\leq n),$$ $$\langle j,\overline{j+1}\rangle=\frac{j(n^2-j^2+2n-2)}{2n^2(2n-1)(n-1)}\quad (1\leq j\leq n-1),$$ $$\langle i,\overline{j}\rangle=\frac{3(i-j)(i+j-1)}{4n^2(2n-1)(n-1)}\quad (2\leq i\leq n,\ 1\leq j\leq i-1).$$

These formulas would determine all two-point correlations using the stated symmetry identity. The paper explains that its techniques do not determine all correlations, so these formulas are proposed as conjectural extensions of the proved results.