feat: add weak Morse inequalities eval problem#301
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§40 of Knill's "Some Fundamental Theorems in Mathematics" (additional statement; the boxed main is the strong inequality). For a Morse function f on a closed smooth finite-dimensional manifold M, b_k(M) ≤ c_k(f) for every k. Mathlib has the smooth-manifold framework and singularHomologyFunctor but no Morse functions or Betti numbers as a named definition. The Challenge ships seven helper definitions. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the weak Morse inequalities as a new lean-eval challenge problem — §40 of Oliver Knill's Some Fundamental Theorems in Mathematics (an additional statement of the section; the boxed main theorem is the strong inequality, submitted as a companion PR).
For a Morse function
fon a closed smooth finite-dimensional manifoldM:b_k(M) ≤ c_k(f)for everyk,i.e. the
k-th Betti number is bounded by the number of Morse-index-kcritical points.mathlib has the smooth-manifold framework,
mfderiv, higher Fréchet derivatives, andsingularHomologyFunctorbut no Morse functions, Morse index, critical-point counts, Betti numbers (as a named definition), or the weak Morse inequality. The Challenge ships seven auxiliary definitions.🤖 Prepared with Claude Code