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Mathematical analysis reveals that small-scale Pythagorean residuals determine Gaussian curvature jets on smooth Riemannian surfaces, suggesting new geometric reconstruction methods.
This work derives the small-scale Pythagorean residual through order six for rotated geodesic right isosceles triangles on a smooth Riemannian surface. The expansion determines the Gaussian curvature, its covariant gradient, and its covariant Hessian through finite angular-harmonic reconstruction systems. Independent coefficient-separating families establish the universal constants, and a variable-curvature numerical example validates the reconstruction.
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Simone Scaffardi (2026) studied this question.
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