The Lean proof is published, you can download it. The clock definitely is ticking.
Edit: Oh, didn't see the "qualifying outlet" condition. But Poincare was ever just put on arXiv, so arXiv must count as well.
If I recall (too lazy to check) folks made slight improvements to Perelman's work and published it in mainstream journals, satisfying the "qualifying outlet" requirement.
Anyone can put anything on arxiv, it counts the same as printing it on tissue paper.
Publish in academic language means accepted peer-reviewed paper.