feat: add Schoenflies theorem eval problem#306
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§48 of Knill's "Some Fundamental Theorems in Mathematics" (Schoenflies, 1906). Strong form: every Jordan curve in the plane is the image of the unit circle under some self-homeomorphism of ℝ². Faithful encoding of Knill's prose statement that "each complementary region is homeomorphic to the open disk" — the strong form is the result that is actually true and implies the bounded-region claim. Mathlib has Metric.sphere, EuclideanSpace, and Homeomorph, but no Schoenflies theorem, no Jordan curve theorem, no invariance-of-domain machinery in a form that would discharge it. Stateable with zero new definitions. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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This PR adds an eval problem for the Schoenflies theorem (strong form):
for every Jordan curve in the plane there is a self-homeomorphism of
ℝ²carrying the curve to the standard unit circle. §48 of Knill'sSome Fundamental Theorems in Mathematics.
The strong form is the faithful encoding of Knill's prose statement
that "each complementary region is homeomorphic to the open disk" —
the literal version is false for the unbounded region (homeomorphic to
ℝ² ∖ closedBall 0 1, fundamental groupℤ, vs. simply connecteddisk). The strong form here implies the bounded-region claim.
Mathlib has
Metric.sphere,EuclideanSpace, andHomeomorph, butno Schoenflies theorem (
grep -ri 'schoenflies' Mathlib/: no hits),no Jordan curve theorem, no invariance-of-domain machinery in a form
that would discharge it. Stateable with zero new definitions.
No formalization found in any major prover.
🤖 Prepared with Claude Code