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Importance: notable
VerificationAuthor claimAccessible artifact / proof
improved boundai assisted

AI-assisted near-quadratic lower bound for exact-value optimization

Kerger reports Ω(d²/log(d+1)) exact-function-value queries at accuracy Θ(d^−1/2) for deterministic convex Lipschitz minimization over a d-dimensional ball.

Sources for this record

What was already known

The cited lower bound was Ω(d), versus an O(d² log²d) value-only upper bound.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

Kerger explicitly credits GPT 5.6 Sol Pro with solving the mathematical problem, followed by human review and formalization.

Limitations

Deterministic exact-value oracle and accuracy scaling are part of the theorem. This is not a lower bound for every randomized or gradient-based method. AIProofWatch has not compiled the Lean artifact.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.

Accessible artifact / proof

A research manuscript or proof artifact is publicly accessible; availability is not independent checking.

Correction and publication history