In this article we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual-partition formula. Then it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each filter is a free subarrangement satisfying the dual-partition formula. This generalizes the main result in cite{ABCHT} which affirmatively settled a conjecture by Sommers and Tymoczko cite{SomTym}.
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