Breakthrough Tracker record
A short preprint claims the Daykin–Frankl width conjecture
Kada Kálmán Williams presents a proof that every convex subset of the Boolean cube contains an antichain of at least its cardinality times the central-binomial density, confirming a conjecture of Daykin and Frankl from 1983.
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- Stable ID
math-daykin-frankl-conjecture-proof-2026- Revision
math-daykin-frankl-conjecture-proof-2026.v1- Field
- Mathematics · Extremal set theory and combinatorics
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Provisional claimed proof
- Last checked
AI role
The note explicitly says it verifies and communicates an LLM-generated proof and credits GPT-5.6 Sol Pro with generating the proof content. The author presents the argument and assumes responsibility for it.
Record details
- Problem or result
- Daykin and Frankl’s 1983 lower bound on the width of convex subsets of the Boolean cube
- Authors
- Kada Kálmán Williams
- Institutions
- Independent author in Szeged, Hungary
- Result date
- First-version preprint submitted September 2, 2026
Why it matters
The inequality gives the conjectured sharp-scale antichain guarantee for every convex family in the Boolean lattice, resolving a four-decade-old extremal-combinatorics question if the proof holds.
Limits
The argument is a four-page first-version preprint generated by an LLM and communicated after author verification. No peer review, independent proof, formal artifact or specialist correctness assessment was located.
Sources
Correction and revision history
- 2026-09-04 — Added after primary-source, scope, status, AI-role and limitation review.
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