The kernel-exhaustion conjecture for the six-parameter channel equation

Consider the integer-polynomial coefficient vectors $d_\phi(\alpha)$ for the six-parameter channel equation, and the kernel relations supplied by Lemma.

Kernel-exhaustion conjecture. The relations of Lemma exhaust the kernel of the channel equation. The claim concerns the completeness of the listed linear relations among channel solutions. It is stated without a resolution status in the source and remains open in this database.