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Geometric split-count research benchmark
Family 183: Power savings for planar halving lines and <i>k</i>-sets. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Geometry and learning-theory researchers can compare planar halving pairs and linearly separable k-subsets to new count bounds.
Applicability and commercial boundary
The constants and saving exponents are nonquantitative; no practical classifier runtime improvement follows. The selected scope covers halving pairs and specific level switches rather than all later k-set claims.
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 a finite counting benchmark without presenting the asymptotic exponent as a measured speedup.
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.