Mazur's $R=\bold T$ conjecture

Let $p$, the finite field $k$, the deformation data $\mathcal D$, the absolutely irreducible type-$\mathcal D$ representation $\bar\rho:G_{\bold Q}\to\operatorname{GL}_2(k)$, and the coefficient ring $\mathcal O$ be as in the construction of the universal deformation ring $R$ and universal Hecke algebra $\bold T$. Let $\varphi:R\to\bold T$ be the natural surjective homomorphism induced by the universal modular deformation. Mazur's $R=\bold T$ conjecture. The map

$$\varphi:R\to\bold T$$

is an isomorphism. The conjecture is the algebraic reformulation of the preceding modularity-lifting statement; the source supplies no resolution status for it.