Conjecture on -Antichains in the Unit Cube
A subset of the pointwise-ordered cube is a -antichain when it meets every chain in at most points. The conjecture concerns the largest possible -dimensional Hausdorff measure of such a set; it is settled here, following work of Janzer.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Combinatorics
- Posed by
- conjecture in the antichain-measure literature
- Year posed
- —
- Years open
- —
- Solved
- 2026-06-26
- Model
- GPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- John M. Campbell
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper states that the construction carrying the proof is largely based on the author's extensive interactions with GPT-5.5 Pro.
Verification
Single-author arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.28606 - On a conjecture on k-antichains in the unit n-cube