Steurer's Conjecture on Vectors with Small Average Correlation
Steurer conjectured in 2010 that any family of $n$ unit vectors with polynomially small average correlation $\mathbb{E}_{i,j}|\langle v_i,v_j\rangle| \le n^{-\varepsilon}$ contains linear-sized constant-separated sets. Refuted in a strong sense, using sparse high-dimensional expanders.
Exact FrontierDelta
Scope and record
Occurred: May 29, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Steurer's Conjecture on Vectors with Small Average Correlation · Steurer's conjecture
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Farzam Ebrahimnejad
human · human collaborator
Shayan Oveis Gharan
human · human collaborator
GPT-5.5 Pro via an agentic system on Codex
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Shayan Oveis Gharan
This event attributed to Farzam Ebrahimnejad
This event attributed to GPT-5.5 Pro via an agentic system on Codex