Confirmation of the Daykin-Frankl conjecture from a language-model proof
A four-page note verifies and communicates a language-model-generated proof of the 1983 Daykin-Frankl conjecture on incomparable elements in convex subsets of the Boolean lattice.
- Lab
- Independent
- Model
- GPT-5.6 Sol Pro
- Field
- Mathematics
- Date
- 2026-09-02
- Human collaborators
- Kada Williams
- Problem posed
- 1983 · open 43 yrs
Sources
Original work
Independent commentary
What was found
Daykin and Frankl conjectured in 1983 that a convex subset P of the n-dimensional Boolean lattice contains at least |P| times the central binomial coefficient divided by 2 to the n pairwise incomparable elements. The note's abstract states its provenance in one sentence: 'We verify and communicate an LLM-generated proof of this conjecture.' The argument proves a stronger product inequality for convex subsets and recovers the original conjecture as a special case, by an induction on dimension resting on a convexity lemma.
Novelty check
The conjecture is named and dated to 1983, due to David E. Daykin and Peter Frankl, and no prior proof was found in the four registries or the surrounding literature on the Boolean lattice. The note presents itself as a first proof rather than a rediscovery, and the strengthened product inequality it proves does not appear in the prior literature located. The result is new.
Caveats and known objections
A four-page unrefereed preprint, checked by its human author and by nobody independent, with no formalization. The human role as stated is verification and communication rather than discovery, which is why autonomy is graded ai-led: the model produced the proof content and the author checked and wrote it up. The model is named in the note's body rather than the abstract. What 'verify' amounts to here is not spelled out, and for a short combinatorial argument the distinction between a careful check and a read matters; treat the proof as needing an independent reading.
Also recorded at
vibematheddaykin-frankl-conjecture
Nothing mechanically. It is a parallel listing of the same result, carrying its own verification label rather than an independent check.
Nobody outside the lab has checked this yet.
Reading the primary source closely enough to say whether it supports the claim counts as a check, and you are credited on the entry.
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-led.
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Graded author verified for verification and ai-led for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Confirmation of the Daykin-Frankl conjecture from a language-model proof. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-02-daykin-frankl-conjectureBibTeX
@misc{whataifound-independent-2026-conjecture,
title = {Confirmation of the Daykin-Frankl conjecture from a language-model proof},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Author verified. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-09-02-daykin-frankl-conjecture}
}