Open statements with known solutions

The following declarations are marked `research open`, but known results
already settle them.

## Published results

- [ ] [OEIS A287616 — `conjecture`](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/OEIS/287616.lean)
— [Theorem 1](https://arxiv.org/abs/2606.26035) proves the exact statement → mark solved.

- [x] [Green 3 — `green_3`](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/GreensOpenProblems/3.lean)
— [Theorem 1.1](https://arxiv.org/abs/2607.06073) gives answer `True` → mark solved.

- [ ] [Green 31 — two upper bounds](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/GreensOpenProblems/31.lean)
— [Theorem 1.1](https://arxiv.org/abs/2607.01169) gives the required improved bound → mark both solved.

- [ ] [AME(7,6) and AME(7,10)](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/OpenQuantumProblems/35.lean)
— [Theorem 1](https://arxiv.org/abs/2608.01011) proves `AME(7,d)` for every `d ≥ 3` → answer `True`.

- [ ] [AME(12,5)](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/OpenQuantumProblems/35.lean)
— [Theorem 2](https://arxiv.org/abs/2608.05781) proves existence → answer `True`.

- [ ] [Independent Domination — even and odd](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Arxiv/2107.00295/IndependentDomination.lean)
— [Corollary 1.3](https://arxiv.org/abs/2202.09594) proves both displayed bounds → mark solved.

- [ ] [MathOverflow 31809](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Mathoverflow/31809.lean)
— [Theorem 1.2](https://arxiv.org/abs/2608.09777) gives a counterexample → answer `False`.

## Already implied in the repository

- [ ] [Green 19 — `lower` and `upper`](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/GreensOpenProblems/19.lean)
— the same file already has the solved theorem `C = 4` → mark both solved.

- [ ] [Erdős 272 — main asymptotic](https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/272.lean)
— the solved Szabó bound in the same file implies main term `N²/2` → mark solved.

This list was prepared with AI assistance and may contain mistakes.

Review the linked Lean files and each cited paper, starting with the declarations listed under Published results. Verify that the cited results really settle each statement, including the repository-implied cases, then update the affected answers or solved status; done means every supported item accurately reflects its known result and questionable claims are left unresolved.

Written by the indexing model from the issue text.