feat: add Koszul formula eval problem#299
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§38 of Knill's "Some Fundamental Theorems in Mathematics" (additional statement; the boxed main theorem is Levi-Civita). For any smooth torsion-free metric-compatible covariant derivative, 2⟨∇_X Y, Z⟩ is the cyclic sum of directional derivatives minus the Lie-bracket cyclic sum — the identity that forces uniqueness of Levi-Civita. Mathlib has the covariant-derivative / Lie-bracket machinery but neither metric-compatibility nor Koszul. The Challenge ships IsMetricCompatible. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the Koszul formula as a new lean-eval challenge problem — §38 of Oliver Knill's Some Fundamental Theorems in Mathematics (an additional statement; the boxed main theorem is the Levi-Civita fundamental theorem, submitted as a companion PR).
For any smooth torsion-free metric-compatible covariant derivative
covon the tangent bundle of a Riemannian manifold:2 ⟨∇_X Y, Z⟩ = X·⟨Y,Z⟩ + Y·⟨X,Z⟩ − Z·⟨X,Y⟩ − ⟨X,[Y,Z]⟩ − ⟨Y,[X,Z]⟩ + ⟨Z,[X,Y]⟩This is the identity that forces uniqueness of the Levi-Civita connection.
mathlib has the covariant-derivative / Riemannian-bundle / Lie-bracket machinery but no metric-compatibility predicate and no Koszul formula. The Challenge ships one auxiliary definition (
IsMetricCompatible).🤖 Prepared with Claude Code