Ramsey forcing-scale reference

Family 160: Superexponential van der Waerden numbers. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Researchers can study lower bounds for the interval sizes needed to force monochromatic arithmetic progressions.

Applicability and commercial boundary

Large asymptotic lower bounds do not build compact codes or optimize a finite scheduling problem without an effective construction.

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

Inspect the explicit coloring construction and finite runtime.

Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Quantitative Superexponential Bounds for van der Waerden Numbers.