Fargues's strong noetherianity conjecture for the Banach algebras $B_I$

Let $E/\mathbb{Q}_p$ be a finite extension, let $F$ be as in the construction of the Fargues–Fontaine curve, and let $I\subset (0,1)$ be a closed interval. Write $B_I$ for the associated Banach algebra.

Fargues's conjecture. The Banach algebra $B_I$ is strongly noetherian: for every $n\geq 1$, the Tate algebra

$$B_I\langle T_1,\dots,T_n\rangle$$

is noetherian.

Strong noetherianity is a foundational finiteness property for the analytic geometry of the Fargues–Fontaine curve and its associated adic spaces. The source attributes this conjecture to Fargues; no resolution is given in the supplied text.