Alpöge is on a roll, with the Jacobian conjecture counterexample, Hadamard matrices <2000, elliptic curves of ranks 30 & 31, and now a claim that S^6 admits a complex structure.

Will any of his results be shown false? To qualify he must post the result on X. The claim can be implicit as long as it’s strongly implicit and broadly, understood to be making a specific claim.

• YES if, by August 31, there is a consensus in credible reporting or within the academic community that at least one of the core arguments or main theorems in his claims are fatally flawed or incorrect. Otherwise, resolves NO.

  • "Flawed" means a core mathematical or theoretical error is identified that invalidates the main result of the tweet, and the error is either unfixable or difficult to patch.

  • Nitpicks—such as minor typos, formatting errors, minor translation gaps in the Lean formalization that do not undermine the mathematical proof's validity, or easily patchable edge cases—do not count toward a YES resolution.