Conjecture on generators of the kernel of the representation functor

Let the diagrammatic category and its representation functor be as in the paper. The kernel is understood as a pivotal category ideal, and the elements described in Theorems $\mathrm{I=H}$, square-switch, and Kekulé are the specified families of relations. Kernel-generation conjecture. The kernel of the representation functor is generated, as a pivotal category ideal, by the elements described in those three theorems. This conjecture would give a complete set of pivotal-category-ideal generators for the relations that vanish under the representation functor; the paper presents it as an unproved conjecture.