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Spectral geometry width research planner
Family 336: Spectral scalar curvature, Urysohn width, and macroscopic dimension. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Geometry researchers can study dimension-reducing maps under the precise spectral scalar-curvature inequality.
Applicability and commercial boundary
A continuous map with bounded entire fibers need not be efficiently constructible or preserve reconstruction accuracy of finite data. The quadratic-form hypothesis requires evidence.
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 constructible example before treating the map as a compression tool.
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.