What was already known
Klopp and Zadik had a minimax-rate node-private exact-recovery method with exponential runtime. Other computationally feasible node-private methods addressed weaker consistent recovery. The paper explicitly frames the polynomial-time minimax-rate combination as the open question.
AI involvement
The authors credit ChatGPT 5.5 Plus with the initial polynomial-time algorithm idea and proof outlines. They corrected and completed the analysis and explain the final estimator.
The declaration identifies ChatGPT's initial polynomial-time algorithm idea as critical; the authors completed and corrected the proof.
Importance
Closes a stated computational gap for private exact recovery under the paper’s assumptions.
Limitations
A truncated variant trades a larger privacy parameter for worst-case polynomial runtime. The authors corrected and rigorized the model’s initial idea, but no separately completed theorem-specific check is documented.
Technical verification
The paper contains a full proof but documents no completed independent or author checking procedure for the final theorem. Reported is the evidence default, not a failed check.
Human understanding
The human authors describe the central score-surrogate and certified rejection-sampling mechanism and its analysis.
Correction and publication history
ChatGPT supplied the initial polynomial-time algorithm idea; the authors completed its analysis.
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