What is the largest $A\subseteq\{1,\dots,N\}$ such that all subset sums $\sum_{n\in S}1/n$ (over $S\subseteq A$) are distinct?

At Formal Conjectures commit 59f30aa314ba225fcd9268723ce8291616df1ab0, the Lean development starfleet/erdos-321 establishes a two-sided asymptotic bound on extremalSize, which denotes the same quantity as Formal Conjectures' Erdos321.R and therefore supplies a candidate answer for the exact occurrence Erdos321.erdos_321.variants.isTheta, not a proof of it. For occurrence resolution only, the exact occurrences Erdos321.erdos_321 and Erdos321.erdos_321.variants.isTheta are associated with problem:erdos:321 under resolver root sha256:a9d6787719c5c8069a9e14ade0f5a62975410272e6cd1583865b282d1d8669dd. At the exact retained Erdős 321 source revisions, the terminal theorem and structural comparison do not establish implication to either fixed Nat.log variant.