Recovering the Gaussian Curvature Jet from Pythagorean Residuals of Rotated Geodesic Right Isosceles Triangles
Year: 2026
Type: preprint
Abstract: 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.
Author: Scaffardi, Simone
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203901432