---
id: "2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt"
url: "https://postcutoff.com/e/2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt/"
as_of: "2026-11-09T21:13:00+01:00"
date: "2026-11-04"
date_precision: day
category: science
importance: 3
confidence: medium
status: [Awaiting review]
verification: Preprint only
sources: 1
editor: human editor
human_review: null
version: "2026-11-04"
---

As of: 2026-11-09 21:13 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-11-04-amplituhedron-magic-number-conjecture-counterexample-chatgpt/

# Amplituhedron magic number conjecture: counterexample found by ChatGPT

Full title: Amplituhedron tiling with fewer tiles than the 'magic number': Akhmedova, Lam and Yost-Wolff report counterexamples 'first discovered by ChatGPT'

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]). The tiling uses an injective cell of degree two. 'Counterexamples to [GL, Conjecture 3.9] were first discovered by ChatGPT.' They conjecture that the degree-weighted count is always the magic number.

## 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

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 188 days after its cutoff
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- Grok 4.7 (training cutoff May 2026): 157 days after its cutoff

## Sources

1. [arXiv 2611.05216: Two examples in amplituhedron tilings](https://arxiv.org/abs/2611.05216) (arxiv.org, paper)

## Changes

- 2026-11-04 (filed): Created from the arXiv PDF

## Related

- 2026-11-04: [AI-assisted results, 4 Nov: arXiv of 4 Nov and Hexagon of 2–3 Nov](https://postcutoff.com/e/2026-11-04-ai-assisted-results-november-4-listing/index.md)
- People: [Thomas Lam](https://postcutoff.com/person/thomas-lam/)