The finitely presented Burnside problem: is every finitely presented periodic group finite?

Claims Theorem 1.1: there is a finitely presented graded $\mathbb F_2$-algebra $R$ such that $\mathrm{St}_{12}(R)$ is infinite, ordinarily finitely presented and periodic; Corollary 1.2 adds Kazhdan's property (T), so it is nonamenable. The companion claims $\mathrm{St}_{12}(R)$ is residually finite and that the kernel $G$ of the map to $\mathrm{St}_{12}(\mathbb F_2)$ is an infinite finitely presented residually finite 2-group, necessarily of unbounded exponent. It does NOT give a finitely presented infinite group of bounded exponent (the bounded Burnside question for finite presentations), and element orders depend on the element.

Claims Theorem 1.1: there is a finitely presented graded $\mathbb F_2$-algebra $R$ such that $\mathrm{St}_{12}(R)$ is infinite, ordinarily finitely presented and periodic; Corollary 1.2 adds Kazhdan's property (T), so it is nonamenable. The companion claims $\mathrm{St}_{12}(R)$ is residually finite and that the kernel $G$ of the map to $\mathrm{St}_{12}(\mathbb F_2)$ is an infinite finitely presented residually finite 2-group, necessarily of unbounded exponent. It does NOT give a finitely presented infinite group of bounded exponent (the bounded Burnside question for finite presentations), and element orders depend on the element.