Mock theta functions' parity-type conjecture

Let $g(q)$ be a mock theta function with integer coefficients, and let $c(g;n)$ denote the coefficient of $q^n$ in its series expansion. Say that $g$ is of parity type $(\frac{1}{2},\frac{1}{2})$ if the proportions of indices $n\geq 0$ for which $c(g;n)$ is even and odd are respectively $\frac{1}{2}$ and $\frac{1}{2}$, and of parity type $(\frac{3}{4},\frac{1}{4})$ if those proportions are respectively $\frac{3}{4}$ and $\frac{1}{4}$. Mock theta functions' parity-type conjecture. The $19$ functions $\mu^{(2)}(q)$, $f^{(3)}(q)$, $\phi^{(3)}(q)$, $\chi^{(3)}(q)$, $\phi_0^{(5)}(q)$, $\phi_1^{(5)}(q)$, $\chi_0^{(5)}(q)$, $\chi_1^{(5)}(q)$, $\phi^{(6)}(q)$, $\psi^{(6)}(q)$, $\gamma^{(6)}(q)$, $\mathcal{F}_0^{(7)}(q)$, $\mathcal{F}_1^{(7)}(q)$, $\mathcal{F}_2^{(7)}(q)$, $S_0^{(8)}(q)$, $S_1^{(8)}(q)$, $U_0^{(8)}(q)$, $X^{(10)}(q)$, and $\chi^{(10)}(q)$ are all of parity type $(\frac{1}{2},\frac{1}{2})$. The four functions $f_0^{(5)}(q)$, $f_1^{(5)}(q)$, $2\mu^{(6)}(q)$, and $\lambda^{(6)}(q)$ are all of parity type $(\frac{3}{4},\frac{1}{4})$. The conjecture is based on computations and known properties; for the latter four functions, one parity subsequence is almost always even and the complementary subsequence is odd half of the time. The paper also notes that the assertion for $\psi^{(6)}(q)$ is equivalent to the assertion for $\lambda^{(6)}(q)$.