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Spectral nodal-set scope and mesh benchmark
Family 350: Yau’s nodal bounds: surfaces and higher dimensions. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Spectral solver researchers can distinguish the sharp surface nodal-length law from its failure in higher dimensions.
Applicability and commercial boundary
The surface constant depends on the fixed metric, and numeric zero contours require resolution control. The selected dimension-five scope proves an unbounded square-root ratio, not automatically the broader power-law headline.
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
Build a fixed-surface eigenmode fixture and keep higher-dimensional exclusions separate.
Evidence scope
The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected; family 354’s explicit main profile formula was read. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.