lean artifact · pending
Artifact ↗Source authenticated
The Euclidean-complete affine Bernstein problem in dimensions three through nine
Claims: for , every smooth affine maximal graph with positive-definite Hessian over an open convex domain whose graph is complete for the induced Euclidean metric is entire and quadratic, so an elliptic paraboloid; no growth or affine-completeness assumption. Via Trudinger-Wang it extends to affine-complete immersed hypersurfaces. The companion constructs a smooth nonquadratic entire solution with positive-definite Hessian in dimension ten, so the range cannot extend to . Dimensions are not addressed, and the dimension-ten example asserts no uniform Hessian bound or affine completeness.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Euclidean-complete affine Bernstein problem in dimensions three through nine · Affine Bernstein in dimensions 3-9
Confidence: Not scored
Registry verification: lean checked · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Companion: A Smooth Nonquadratic Entire Affine Maximal Graph in Dimension Ten evidence for this event
This event attributed to Unreleased internal OpenAI model
The Euclidean-complete affine Bernstein problem in dimensions three through nine evidence for this event
VibeMathed record: The Euclidean-complete affine Bernstein problem in dimensions three through nine evidence for this event
The Euclidean-complete affine Bernstein problem in dimensions three through nine parent of this event
Lean Comparator challenge AffineBernstein (not in formalization.yaml) evidence for this event
Claims: for , every smooth affine maximal graph with positive-definite Hessian over an open convex domain whose graph is complete for the induced Euclidean metric is entire and quadratic, so an elliptic paraboloid; no growth or affine-completeness assumption. Via Trudinger-Wang it extends to affine-complete immersed hypersurfaces. The companion constructs a smooth nonquadratic entire solution with positive-definite Hessian in dimension ten, so the range cannot extend to . Dimensions are not addressed, and the dimension-ten example asserts no uniform Hessian bound or affine completeness. parent of this event
Lean solution module OAI/Analysis/AffineBernstein/Main.lean evidence for this event
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