feat: add 3D smooth Poincaré conjecture (Perelman) eval problem#294
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feat: add 3D smooth Poincaré conjecture (Perelman) eval problem#294kim-em wants to merge 1 commit into
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This PR adds the 3D smooth Poincaré conjecture as a new eval problem: every simply connected compact Hausdorff smooth 3-manifold is diffeomorphic to 𝕊³. Recorded in mathlib as `proof_wanted SimplyConnectedSpace.nonempty_diffeomorph_sphere_three`. The smooth-category strengthening of the topological 3D Poincaré; also Perelman 2002-2003 (in dim 3 the smooth and topological versions are equivalent via Moise's theorem, but the Lean statement carries the smooth structure explicitly). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds the 3D smooth Poincaré conjecture as a new lean-eval challenge problem: every simply connected compact Hausdorff smooth 3-manifold is diffeomorphic to
𝕊³.Recorded in mathlib as
proof_wanted SimplyConnectedSpace.nonempty_diffeomorph_sphere_threeinMathlib/Geometry/Manifold/PoincareConjecture.lean. The smooth-category strengthening of the topological 3D Poincaré conjecture; also due to Perelman 2002–2003. In dimension 3 the smooth and topological versions are equivalent (Moise's theorem says every topological 3-manifold admits a unique smooth structure), but the Lean statement carries the smooth structure explicitly viaIsManifold (𝓡 3) ∞ Mand concludes with a diffeomorphismM ≃ₘ⟮𝓡 3, 𝓡 3⟯ 𝕊³.Companion problem: #293 is the topological form. mathlib has the differential-topology scaffolding but neither Ricci flow nor Moise's theorem.
🤖 Prepared with Claude Code