This article proposes a path toward the proof of the Riemann Hypothesis using the following elementary and direct equivalent formulation; the Riemann Hypothesis is equivalent to:
$$
\sum_{k \in \mathbb{N}} \frac{\left(\frac{1}{1}+\dots+\frac{1}{n}\right)^k}{k!} \textstyle \left(\frac{1}{k}+\dots+\frac{1}{k^2}\right) > \displaystyle \sum_{d|n} d
$$
for all $n \in \mathbb{N}$.
Writing $\frac{H_n^k}{k!}$ in this unique and magnificent, so powerful and useful form using the Young's Lattice and $H_n^{\mathbf{\lambda}}$, the $n$-th generalized harmonic number of order $\lambda_1+ \dots+ \lambda_m=k$ associated with the partition $\mathbf{\lambda}=(\lambda_1, \dots, \lambda_m) \vdash k$:
\[
\frac{H_n^k}{k!} = \sum_{\mathbf{\lambda} \, \vdash \, k} \frac{H_n^{\mathbf{\lambda}}}{\mathbf{\lambda}!}.
\]
Employing the partition-based version of the Assembly Theorem, wich establishes that for all $n, m \in \mathbb{N}$, the following identity holds:
\[
\mathfrak{S}_n^{m} := \sum_{k=1}^n \sum_{\mathbf{\lambda} \in \wp_k^{k+m-1}} H_n^{\mathbf{\lambda}} = n.
\]
And finally assembling divisors using all the partitions of the Assembly Set:
\[
\frac{1}{\mathbf{\Lambda}!}\sum_{k=1}^n \sum_{\mathbf{\lambda} \in \wp_k^{k+m-1}} H_n^{\mathbf{\lambda}} = \frac{n}{\mathbf{\Lambda}!} = d.
\]
Publication Date: 2026-06-14