Scalar curvature and topology assumption ledger

Family 335: Gromov’s integral scalar-curvature bound for simplicial volume. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometric researchers can relate negative scalar-curvature integrals, simplicial volume and positive-curvature topological restrictions.

Applicability and commercial boundary

The dimension constant and exact global smooth/topological hypotheses are not finite mesh curvature certificates or shape-design algorithms.

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

Identify an exact manifold with computable simplicial volume and curvature integral.

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.

An integral scalar curvature bound for real simplicial volume.