Buzzard's slope conjecture for modular forms

Let $p>3$ and $N$ be as above, and suppose that $p$ is $\Gamma_0(N)$-regular, meaning that the conditions on the eigenvalues of $T_p$ in weights up to $k_p$ hold as specified above. Let $s_2,s_4,\ldots$ be the integer sequences produced by Buzzard's algorithm, and let $v_2,v_4,\ldots$ denote the sequences of $p$-adic valuations of the eigenvalues of $T_p$ acting on $S_k(\Gamma_0(N))$. Buzzard's slope conjecture. Assume that $p$ is $\Gamma_0(N)$-regular. Then the sequences $s_2,s_4,\ldots$ of integers are precisely the sequences $v_2,v_4,\ldots$ of $p$-adic valuations of $T_p$ acting on $S_k(\Gamma_0(N))$. This conjecture predicts that Buzzard's combinatorial algorithm exactly determines the $p$-adic slopes of modular forms of fixed level and varying even weight; the source gives no resolution status for this statement.