Correction to: Nature Communications https://doi.org/10.1038/s41467-022-30079-z, published online 09 May 2022

The PDF version of this article contained an error in equation 12. The M matrix in equation 12 was incorrectly formatted as a row vector where they should form a square matrix.

This has to be corrected only in the PDF version of the article, the HTML version is Ok.

How it appears now:

$${\omega }_{n}\left(\begin{array}{c}{{{{\bf{F}}}}}_{n}^{\rightharpoonup }\\ {{{{\bf{F}}}}}_{n}^{\leftharpoonup }\end{array}\right)=({{\mathbb{M}}}_{{\rightharpoonup }_{,n}}^{\rightharpoonup }{{\mathbb{M}}}_{{\leftharpoonup }_{,n}}^{\rightharpoonup }{{\mathbb{M}}}_{{\rightharpoonup }_{,n}}^{\leftharpoonup }{{\mathbb{M}}}_{{\leftharpoonup }_{,n}}^{\leftharpoonup })\left(\begin{array}{c}{F}_{n}^{\rightharpoonup }\\ {{{{\bf{F}}}}}_{n}^{\leftharpoonup }\end{array}\right)$$

How it should appear:

$${\omega }_{n}\left(\begin{array}{c}{{{{\bf{F}}}}}_{n}^{\rightharpoonup }\\ {{{{\bf{F}}}}}_{n}^{\leftharpoonup }\end{array}\right)=\left(\begin{array}{cc}{{\mathbb{M}}}_{{\rightharpoonup }_{,n}}^{\rightharpoonup } & {{\mathbb{M}}}_{{\leftharpoonup }_{,n}}^{\rightharpoonup }\\ {{\mathbb{M}}}_{{\rightharpoonup }_{,n}}^{\leftharpoonup } & {{\mathbb{M}}}_{{\leftharpoonup }_{,n}}^{\leftharpoonup }\end{array}\right)\left(\begin{array}{c}{{{{\bf{F}}}}}_{n}^{\rightharpoonup }\\ {{{{\bf{F}}}}}_{n}^{\leftharpoonup }\end{array}\right)$$