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We characterize Weihrauch reducibility in E-PA$^{\omega}$ + QF-AC$^{0,0}$ andall systems containing it by the provability in a linear variant of the samecalculus using modifications of G\"odel's Dialectica interpretation thatincorporate ideas from linear logic, nonstandard arithmetic, higher-ordercomputability, and phase semantics.

The characterization of Weihrauch reducibility in systems containing E-PA$^{\omega}$ + QF-AC$^{0,0}$