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feat: add Smale conjecture eval problem - #18

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kim-em merged 3 commits into
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eval/smale-conjecture
Apr 17, 2026
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feat: add Smale conjecture eval problem#18
kim-em merged 3 commits into
mainfrom
eval/smale-conjecture

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@kim-em kim-em commented Apr 17, 2026

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Summary

  • Adds the Smale conjecture (Hatcher 1983) as a new eval problem in the relative parameterized form: smooth families of self-diffeomorphisms of S³ on a compact manifold-with-boundary X, whose boundary restriction already factors through O(4), deform rel ∂X to families fully factoring through O(4).
  • This relative form captures π_k(Diff(S³), O(4)) = 0 for all k, which is equivalent (modulo smoothing theory) to the homotopy equivalence O(4) ≃ Diff(S³). The non-relative version would only give surjectivity on π_*.
  • The Cerf case (X = point, ∂X = ∅) is the unparameterized theorem from feat: add Cerf's theorem Γ₄ = 0 eval problem #17.
  • Uses (𝓡∂ n).boundary X from mathlib's InteriorBoundary API to express the boundary condition, with [NeZero n] required by mathlib for this to elaborate.

🤖 Prepared with Claude Code

kim-em and others added 3 commits April 17, 2026 16:26
Hatcher's 1983 theorem that Diff(S³) ≃ O(4), stated in the relative
parameterized form: smooth families of self-diffeomorphisms of S³ on a
compact manifold-with-boundary X, whose boundary restriction already
factors through O(4), deform rel ∂X to families fully factoring through
O(4). This captures π_k(Diff(S³), O(4)) = 0 for all k, equivalent
(modulo smoothing theory) to the homotopy equivalence.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Resolve conflict in problems.toml: keep both Cerf (from main) and Smale entries.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
@kim-em
kim-em merged commit 3b89046 into main Apr 17, 2026
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