  Local hidden-variable model of singlet-state correlations discussed in M.
Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat to
entangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), is
shown to be a particular case of an infinite hierarchy of local hidden-variable
models based on an infinite hierarchy of calculi. Violation of Bell-type
inequalities is shown to be a `confusion of languages' problem, a result of
mixing different but neighboring levels of the hierarchy. Mixing of
non-neighboring levels results in violations beyond the Tsirelson bounds.
