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Nondegenerate planar point-set research design
Family 191: A power improvement in the Heilbronn triangle lower bound. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Geometric design researchers can explore point sets maximizing the smallest triangle area.
Applicability and commercial boundary
The saving exponent is extremely small; the formal scope covers an unbounded sequence of sizes, while the paper claims all sufficiently large n. This is not a practical mesh-quality guarantee.
Initial business decision
Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.
Next verification action
Extract actual constants and coordinates before proposing a finite sensor or mesh layout.
Evidence scope
The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scopes were additionally inspected; explicit effectiveness passages were inspected for 076, 143 and 178. No independent proof verification was run. Pinned source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.