Signed clique expectation decay conjecture

Let $k$ and $p$ be fixed, let $\mathcal{G}(n,p,d)$ denote the noisy high-dimensional random geometric graph model without edge subsampling, and let $\tau_{[k]}$ be the signed $k$-clique statistic on vertices $[k]$. Signed clique expectation decay conjecture. There exists a constant $C_{k,p}$ such that

$$\left\lvert\operatorname{\mathbb{E}}_{\mathcal{G}(n,p,d)}[\tau_{[k]}]\right\rvert \le \frac{C_{k,p}}{d^{k/6}}.$$

The conjecture would sharpen the dependence on $d$ in the bound for the expected signed clique count and suggests that signed clique statistics cannot improve the detection boundary in the regimes discussed above. Its resolution is not given in the source.