Planar unbounded Tate-defect conjecture for primitive-divergent phi-four graphs

Let $G$ be a primitive-divergent graph in $\phi^4$, with $N_G$ edges, and let $w(G)$ and $\mathfrak{h}(G)$ denote the weight and Hodge quantities associated with the relative de Rham class of its Feynman integrand. Define the Tate defect by

$$td(G)=2\mathfrak{h}(G)-w(G).$$

Unbounded Tate-defect conjecture. There exists a sequence of primitive-divergent graphs $G_i$ in $\phi^4$ such that

$$td(G_i)\longrightarrow\infty.$$

Furthermore, the $G_i$ can be taken to be planar. The claim concerns the expected existence of arbitrarily large non-Tate defects; no resolution is given in the source.