Klopp-Zadik Question on Polynomial-Time Node-Private Recovery

Precise statement

Klopp and Zadik gave an exponential-time node-private algorithm for exact community recovery in stochastic block models and asked whether a polynomial-time algorithm could match it. One can: a Lipschitz surrogate for the penalized likelihood plus an accept-reject sampler gives a high-probability polynomial-time node-private algorithm that nearly matches the exponential-time guarantee.

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

ChatGPT 5.5 Plus

The AI declaration says the paper was written with the model's help and that it played a critical role in brainstorming the initial idea for a polynomial-time algorithm and in providing proof outlines for the main results. Two of the authors are the pair who posed the question.

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

Verification boundary

unreviewed

arXiv preprint; not yet peer-reviewed.

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

Timeline

1. 2026-07-10

   arXiv:2607.09441 - Near-optimal node-private community estimation in polynomial-time

   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

argument (source-reported)

Source-reported tools: argument.

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.