The density hypothesis for the Riemann zeta-function

For $1/2\leq\sigma<1$, let $N(\sigma,T)$ count the zeros $\rho$ of the Riemann zeta-function with $\operatorname{Re}(\rho)\geq\sigma$ and $|\operatorname{Im}(\rho)|\leq T$. Define $\mathrm{A}(\sigma)$ as the infimum of fixed exponents $A$ such that, for infinitesimal $\delta>0$ and unbounded $T$,

$$N(\sigma-\delta,T)\ll T^{A(1-\sigma)+o(1)}.$$

Density hypothesis.

$$\mathrm{A}(\sigma)\leq 2$$

for all $1/2\leq\sigma<1$. This is the standard expected upper bound for the density of zeta zeros to the right of the critical line; the source gives no resolution status.