Amplituhedron magic number conjecture: counterexample found by ChatGPT
Awaiting review
The takeaway
Evgeniya Akhmedova, Thomas Lam and Calvin Yost-Wolff (arXiv 2611.05216) give a tiling of the m = 4 amplituhedron A(11,3,4) with 489 tiles, one fewer than the magic number 490, refuting the strong form of the magic number conjecture ([GL, Conjecture 3.9]).
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 4 November 2026
Your AI and this story
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None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 127 days before it.
Key facts
- Tiling T3 of A(11,3,4) has 489 tiles vs magic number 490, obtained from a BCFW tiling by three bistellar flips
- First known tiling using a cell of degree higher than one; all BCFW cells have degree 1
- New Conjecture 1.6: for even m, the sum of degrees of the cells of any tiling equals the magic number M(k, ℓ, m/2)
- Disclosure: ‘Counterexamples to [GL, Conjecture 3.9] were first discovered by ChatGPT. We further directed ChatGPT to search for the specific counterexamples that are reported here … the data in the appendix was written by ChatGPT under our supervision.’
- Verification: preprint (computational, human-written main text)
What happened
The amplituhedron (Arkani-Hamed and Trnka) encodes scattering amplitudes in N=4 super Yang–Mills. It was conjectured that every tiling of the even-m amplituhedron has the same number of tiles, the “magic number”. The new paper reports a tiling of A(11,3,4) with 489 tiles instead of 490, and says ChatGPT found the first counterexamples. The authors propose that a weighted count (by cell degree) is still invariant.
Why it matters
A senior algebraic combinatorialist (Lam) reports an AI-found counterexample to a conjecture in a field linked to physics. The weaker, degree-weighted form stays open.
What is disputed or not yet verified
| Verification | Unrefereed preprint |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
- arXiv 2611.05216: Two examples in amplituhedron tilingsarxiv.org, paper
Changes
- Filed from the arXiv PDF