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feat: add Cerf's theorem Γ₄ = 0 eval problem - #17

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kim-em merged 1 commit into
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eval/cerf-gamma-four
Apr 17, 2026
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feat: add Cerf's theorem Γ₄ = 0 eval problem#17
kim-em merged 1 commit into
mainfrom
eval/cerf-gamma-four

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

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Summary

  • Adds Cerf's 1968 theorem (Γ₄ = 0) as a new eval problem: every self-diffeomorphism of S³ is smoothly isotopic to the restriction of a linear isometry of ℝ⁴.
  • The isotopy is encoded as a smooth map [0,1] × S³ → S³ with a smooth slice-inverse, which forces each time-slice to be a diffeomorphism without needing a C^∞ topology on Diffeomorph S³ S³ (which mathlib does not yet carry).
  • This is the unparameterized (X = point) case of the Smale conjecture (Hatcher 1983), to be added in a follow-up PR.

🤖 Prepared with Claude Code

Cerf's 1968 theorem: every self-diffeomorphism of S³ is smoothly isotopic
to the restriction of a linear isometry of ℝ⁴. Stated as the existence of
a smooth isotopy [0,1] × S³ → S³ from f to a linear isometry, with smooth
slice-inverse encoding the diffeomorphism property of each time-slice.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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kim-em merged commit 673376f into main Apr 17, 2026
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