Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Nikolov and Ullman asked, as Open Problem 1 on DifferentialPrivacy.org, whether $k$ statistical queries over a universe of size $T$ can be released under pure differential privacy at the square-root error rate that the known lower bounds suggest, rather than the cube-root rate of the classical small-database method. They can: for every $n$ and $\varepsilon > 0$ there is an $\varepsilon$-differentially private mechanism with expected error $O(\min\{1, \sqrt{\log(2T)\log(2k)/(\varepsilon n)}\})$.
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.
The generative-AI disclosure states that Codex and Aristotle were used in connection with Lean formalization and proof search, and that Codex also gave editorial feedback on clarity and organization. Proof search is a mathematical contribution, but the disclosure does not say which steps came from where.
Provider: OpenAI / Harmonic · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint with a companion Lean 4 development that the paper says machine-checks the finite construction, pure privacy after deterministic decoding, and the all-regimes upper bound, with an axiom audit and a paper-to-Lean crosswalk in the artifact. We have not compiled it. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
information-theoretic; a polynomial-time implementation remains open
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.