Conjecture on $k$-Antichains in the Unit Cube

Precise statement

A subset $A$ of the pointwise-ordered cube $[0,1]^n$ is a $k$-antichain when it meets every chain in at most $k$ points. The conjecture concerns the largest possible $(n-1)$-dimensional Hausdorff measure of such a set; it is settled here, following work of Janzer.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5 Pro

The paper states that the construction carrying the proof is largely based on the author's extensive interactions with GPT-5.5 Pro.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Single-author arXiv preprint; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-06-26

   arXiv:2606.28606 - On a conjecture on k-antichains in the unit n-cube

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.