The concatenation conjecture for fermionic-degree-one Macdonald superpolynomials

Let $\Lambda$ be a concatenable superpartition, meaning that it has fermionic degree $m=1$ and satisfies $\Lambda^a_m\geq\Lambda^s_1$. Let $\lambda$ be the partition obtained from $\Lambda$ by removing the semicolon, so $\lambda=(\Lambda^a,\Lambda^s)$. Define the linear map $\phi$ on deformed Schur superpolynomials by

$$\phi(S_\Omega)= \begin{cases} S_\mu,&\text{if }\Omega\text{ is concatenable and }\mu\text{ is its corresponding partition},\\ 0,&\text{otherwise}. \end{cases}$$

Concatenation conjecture. One has

$$\phi(J_\Lambda)=J_\lambda.$$

This conjecture would recover ordinary Macdonald polynomials from the fermionic-degree-one superspace theory through concatenation. It is presented as the second new conjecture for the generalized Kostka coefficients, and remains unproved in the supplied text.