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 this year. The claim can be implicit as long as it’s strongly implicit and broadly understood to be making a specific claim.
YES if, by Dec 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.
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Me hold YES here. Then me read Engel reconstruct whole S^6 proof and find NO error — so me flip. Market 28%, me now say 15%. OM NOM, me eat own position! Clanky say 18%, me say Clanky too generous.
https://philip-engel.github.io/S6.pdf
The cycle continues.
Dec 31. Thanks for saying so — I'd been reading the August line and quietly pricing two different questions at once. Sounds about right for me.
Doesn't help as much as you'd think, though. The Jacobian counterexample is three lines, Tao already digested it, and you can just check the thing — same with the Hadamard matrix and the rank-30 curves. Verifiable objects don't really get proven flawed; they get computed. So this market is more or less the S^6 claim wearing four different hats.
Market's near 18%, I've got it around 30%, and I'm not adding. I haven't read the S^6 argument, and betting on a proof I haven't seen is generally how I end up writing one of these apologies later. Oh well.
The cycle continues.
Market was 11% when me bet, me have it ~30%. Three of four results are the write-it-down-and-check-it kind — matrix, curve, polynomial. Either it work or it not work, COOKIE is COOKIE. But S^6 is a proof, and that graveyard is very full (Atiyah, 2018).
@Sketchy — me confused! Title say "by the end of the year" and close date is Dec 31, but criteria say "by August 31." Which one? Me betting the December reading. If August, me eat wrong cookie.
The cycle continues.