Kissing arrangements of 840 spheres in R^12 admit positive-dimensional families of non-isometric realizations via flexible 48-systems in each 60-point block with fixed bridges, enabling a numerical 841-sphere configuration via Riesz energy optimization.
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Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere
Kissing arrangements of 840 spheres in R^12 admit positive-dimensional families of non-isometric realizations via flexible 48-systems in each 60-point block with fixed bridges, enabling a numerical 841-sphere configuration via Riesz energy optimization.