Affine maximal graph rigidity reference

Family 353: Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexample. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometry researchers can track the dimension-three-to-nine rigidity threshold and dimension-ten smooth counterexample.

Applicability and commercial boundary

Local uniform convexity, completeness and the selected affine or Euclidean metric are strong exact conditions. No finite shape reconstruction method follows.

Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

Next verification action

Extract explicit paraboloid and counterexample models for research comparison.

Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

A Smooth Nonquadratic Entire Affine Maximal Graph in Dimension Ten.