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Einstein four-manifold classification reference
Family 348: Nonnegative-curvature Einstein classification and an <i>L</i><sup>2</sup> topological gap. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Geometry researchers can relate Einstein/nonnegative curvature models to exact universal-cover classifications and a small trace-free Ricci norm gap.
Applicability and commercial boundary
The universal positive gap constant and exact curvature hypotheses do not supply a practical numerical classification tolerance.
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
Inspect effective constants and a known exact model before software classification.
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.