Kronheimer–Mrowka: dodecahedron instanton homology is 64 (ChatGPT Astra 6)
Awaiting review
Importance: major (4 of 5)The takeaway
Peter Kronheimer (Harvard) and Tomasz Mrowka (MIT) deposited on Hexagon (2611.00021, published 3 Nov 2026) a “proposed proof” that the SO(3) instanton homology J♯ of the planar dodecahedron web has dimension 64.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Unverified claim
- Importance
- Major (4 of 5)
- Last verified
- 3 November 2026
Your AI and this story
- GPT-6 Astra187 days after its cutoff
- Claude Opus 5.5126 days after its cutoff
- Gemini 4 Argon217 days after its cutoff
- Grok 4.7156 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 126 days before it.
Key facts
- Claim (abstract): the octahedral diagram reduces dim J♯(D) to 60 or 64; ‘We give a proposed proof that all three [secondary-map coefficients] vanish and that the dimension is 64’
- Context: Kronheimer–Mrowka, ‘Tait colorings, and an instanton homology for webs and foams’ (JEMS 2019, arXiv 1508.07205) defined J♯ and asked whether its dimension equals the number of Tait colourings for planar webs; 64 ≠ 60 would answer that in the negative for the dodecahedron
- Provenance (verbatim): ‘Primarily AI-generated’; ‘Some parts of this contribution, but not all, have been checked and understood by a human’; ‘ChatGPT Astra 6 was prompted to consider the question of whether the instanton homology of the dodecahedron had dimension 60 or 64, having been provided with previous calculations from ChatGPT and Claude.’
- Authorship mode on Hexagon: no-human-author-claimed; sponsor Peter Kronheimer; exact matrices and foam calculations ‘provided separately’
- Verification status: unrefereed Hexagon deposit, described by the authors as a proposed proof; no Lean formalization; no HN discussion found on 3 Nov
What happened
On 2 Nov 2026 Peter Kronheimer deposited, and on 3 Nov Hexagon published, a paper by him and Tomasz Mrowka on the instanton homology of the planar dodecahedron web. Known calculations left two values, 60 and 64; the paper gives a proposed proof that three coefficients of a secondary map vanish, which gives 64. The provenance record says the text is primarily AI-generated by ChatGPT Astra 6, prompted with earlier calculations from ChatGPT and Claude, and that only some parts have been checked by a human.
Why it matters
Kronheimer and Mrowka built J♯ in 2015 as a possible route to the four-colour theorem, asking whether its dimension counts Tait colourings for planar webs. The dodecahedron has 60 Tait colourings, so a dimension of 64 would answer that question in the negative for this web. The result is a proposed proof, not checked in full by its sponsors.
What is disputed or not yet verified
| Verification | Unrefereed Hexagon deposit; partly human-checked |
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Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 2 primary
Primary
Changes
- Filed (Hexagon provenance record read through the Hexagon API)