The conjecture that the Schur–Siegel–Smyth trace constant equals 2

Assess the conjecture that the least limiting trace-to-degree ratio of totally positive algebraic integers equals 2, while noting that the cited work of Smith disproves this conjecture.

Background

The paper studies the least limiting value of the ratio between the trace and degree of totally positive algebraic integers and proves a lower bound of 1.80220, improving the previous bound of 1.80203. It also cites an upper bound of 1.8216. The final remark states that the paper does not address the conjecture that this constant equals 2 and indicates that Smith disproved that conjecture. Thus, the passage records an explicitly named conjecture, although it is presented as already disproved rather than as an unresolved problem.