Carbery's Almost-Orthogonality Inequality in Lp
For , does Carbery's proposed many-function almost-orthogonality inequality hold with the pairwise overlap coefficients raised to the power - and if not, what is the largest possible exponent?
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Functional analysis
- Posed by
- Anthony Carbery
- Year posed
- 2009
- Years open
- 17y
- Solved
- 2026-05
- Model
- Grok Heavy, Grok 4.20 Heavy
- Vendor
- xAI
- Collaborators
- Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili, Jose Madrid, Haozhu Wang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
exponent 2 fails for every p > 2; the sharp exponent p' form is proved for integer p ≥ 2
What the AI did
The authors knew a counterexample should exist from unstructured brute-force search; Grok produced a construction with a clear structural pattern, which revealed the optimal exponent p'.
Verification
Author-checked public arXiv preprint. Not yet peer-reviewed.
Source
arXiv:2605.05192 - Almost-orthogonality in Lp spaces: a case study with Grok