What was already known
The graphical estimate was known in dimension three and in broader convex settings. A dimension-four result depended on a modulus of the gradient; the related Hessian equation had all-dimensional estimates.
AI involvement
ChatGPT Sol 5.6 suggested the central compression inequality and supplied the auxiliary η formula. Qiu and Yan set the framework, checked exploratory calculations and completed the geometric argument.
The disclosure identifies the model-suggested Lemma 3.4 compression inequality, which Remark 3.6 says is needed to keep the corrected matrix admissible and the Jacobi estimate positive; essential human architecture is separately credited.
Importance
The retained model-suggested inequality supports an all-dimensional graphical curvature estimate.
Limitations
Qiu and Yan designed the proof architecture and completed the theorem. The model’s identified contribution is the central compression inequality and auxiliary formula, not the whole proof. No completed proof check is documented.
Technical verification
The authors checked exploratory AI calculations and candidate counterexamples, but those checks are not a documented technical review of the retained Lemma 3.4-to-Theorem 1.1 proof. No completed check of the assessed theorem or machine formalization is cited; Reported is the evidence default.
Human understanding
The human authors explain why vertical comparison fails, how geometric distance and compression repair it, and how separation plus the two-surface Pogorelov estimate give the stated bound. No central mechanism is described as unexplained.
Correction and publication history
The retained model-suggested inequality supports an all-dimensional graphical curvature estimate.
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