The forcing conjecture for bipartite graphs

Corollary 1.3: for the same connected bipartite $H$ (which contains cycles) there are $p\in(0,1)$ and a nonconstant graphon $W$ with $t(K_2,W)=p$ and $t(H,W)=p^{66}$; sampling gives finite graphs with edge and $H$-densities tending to $p$ and $p^{66}$ but four-cycle density tending to a limit above $p^4$. So $H$ is not $p$-forcing at that $p$, and the conjecture fails. Since the forcing conjecture implies Sidorenko's, this follows from the Sidorenko counterexample; no separate idea is claimed.

Corollary 1.3: for the same connected bipartite $H$ (which contains cycles) there are $p\in(0,1)$ and a nonconstant graphon $W$ with $t(K_2,W)=p$ and $t(H,W)=p^{66}$; sampling gives finite graphs with edge and $H$-densities tending to $p$ and $p^{66}$ but four-cycle density tending to a limit above $p^4$. So $H$ is not $p$-forcing at that $p$, and the conjecture fails. Since the forcing conjecture implies Sidorenko's, this follows from the Sidorenko counterexample; no separate idea is claimed.