feat: add Cauchy–Kovalevskaya theorem eval problem#272
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This PR adds the Cauchy-Kovalevskaya theorem (§32 of Knill's "Some Fundamental Theorems in Mathematics") as a new eval problem: the quasi-linear scalar Cauchy problem with real-analytic data has a unique local analytic solution. The statement uses only off-the-shelf mathlib, encoding the PDE through the Fréchet derivative; mathlib has no Cauchy-Kovalevskaya theorem. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the Cauchy–Kovalevskaya theorem as a new lean-eval challenge problem — §32 of Oliver Knill's Some Fundamental Theorems in Mathematics.
For real-analytic data
F,f,u₀, the quasi-linear scalar Cauchy problemuₜ = F·∇ₓu + f,u(·,0) = u₀has a unique local analytic solution near every point of the initial hypersurface.The statement uses only off-the-shelf mathlib (
AnalyticOnNhd,fderiv,EuclideanSpace) — no new definitions. The PDE is encoded through the Fréchet derivative:fderiv ℝ u p (0,1)is the time derivative andfderiv ℝ u p (v,0)the spatial directional derivative. Locality and uniqueness are folded into one∀ x₀, ∃ U …statement. Mathlib has no Cauchy–Kovalevskaya theorem, and a search found no formalization of it in any other proof assistant.🤖 Prepared with Claude Code