feat: add Milnor's exotic 7-sphere eval problem#292
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This PR adds Milnor's 1956 theorem on the existence of a smooth 7-manifold homeomorphic but not diffeomorphic to 𝕊⁷ as a new eval problem. Recorded in mathlib as `proof_wanted exists_homeomorph_isEmpty_diffeomorph_sphere_seven` in `Mathlib/Geometry/Manifold/PoincareConjecture.lean`. Birth of differential topology as a distinct subject. Mathlib has ChartedSpace, IsManifold, Diffeomorph, and the unit sphere as a smooth manifold but no exotic-sphere construction. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds Milnor's exotic 7-sphere as a new lean-eval challenge problem — the existence of a smooth 7-manifold homeomorphic to the standard
𝕊⁷but not diffeomorphic to it.Recorded in mathlib as
proof_wanted exists_homeomorph_isEmpty_diffeomorph_sphere_seveninMathlib/Geometry/Manifold/PoincareConjecture.lean. Milnor's 1956 discovery (Ann. of Math. 64) — the birth of differential topology as a distinct subject. The classical construction usesS³-bundles overS⁴; non-diffeomorphism is detected by Milnor's λ-invariant built from the signature of an 8-manifold bounding the candidate (Hirzebruch's signature theorem + an integrality argument mod 7).mathlib has
ChartedSpace,IsManifold,Diffeomorph, and the unit sphere as a smooth manifold (Geometry/Manifold/Instances/Sphere.lean) but no exotic-sphere construction.🤖 Prepared with Claude Code