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We show that pairs $(X,Y)$ of 1-spherical objects in $A_\infty$-categories,such that the morphism space ${\rm Hom}(X,Y)$ is concentrated in degree 0, canbe described by certain noncommutative orders over (possibly stacky) curves. Infact, we establish a more precise correspondence at the level of isomorphism ofmoduli spaces which we show to be affine schemes of finite type over ${\BbbZ}$.

$A_\infty$-structures associated with pairs of 1-spherical objects and noncommutative orders over curves