feat: add fundamental theorem of Riemannian geometry (Levi-Civita) eval problem#298
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feat: add fundamental theorem of Riemannian geometry (Levi-Civita) eval problem#298kim-em wants to merge 1 commit into
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…al problem §38 of Knill's "Some Fundamental Theorems in Mathematics". On a C^∞ finite-dimensional Riemannian manifold there exists a unique smooth torsion-free metric-compatible covariant derivative (the Levi-Civita connection). Mathlib has the covariant-derivative / Riemannian-bundle machinery but no metric-compatibility predicate and no Levi-Civita existence/uniqueness. The Challenge ships two helper defs (IsMetricCompatible, SameOnSmooth). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the fundamental theorem of Riemannian geometry (Levi-Civita) as a new lean-eval challenge problem — §38 of Oliver Knill's Some Fundamental Theorems in Mathematics.
On a
C^∞finite-dimensional Riemannian manifold(M, g), there exists a unique smooth torsion-free metric-compatible covariant derivative onTM— the Levi-Civita connection. Uniqueness is stated on the smooth-section subspace via aSameOnSmoothpredicate (mathlib'sCovariantDerivativeis bundled over all sections, not just smooth ones).mathlib has
CovariantDerivative,CovariantDerivative.torsion,ContMDiffCovariantDerivative,RiemannianBundle,IsContMDiffRiemannianBundle, andextDerivFun— but no metric-compatibility predicate and no Levi-Civita theorem. The Challenge ships two auxiliary definitions:IsMetricCompatibleandSameOnSmooth.🤖 Prepared with Claude Code