Symbol-based residual certification of reduced and neural surrogates for tempered-fractional CGMY pricing

We certify reduced and neural approximations of European-put price trajectories under the Carr--Geman--Madan--Yor model by residual bounds for the spline Galerkin discretisation of the tempered-fractional pricing equation. The Galerkin matrices are Toeplitz sections of an explicit periodised Fourier symbol; summing the alias series to a stated tail makes the assembled system exact to $10^{-8}$. A

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