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Arithmetic progression density reference
Family 159: Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi bounds. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Additive-combinatorics researchers can compare finite progression-free sets to the stated fixed-length density upper bounds.
Applicability and commercial boundary
Reciprocal-sum divergence is an infinite condition; constants and exponents may be impractical, and no fast progression-search procedure is supplied.
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 effective fixed-k constants before a finite planning tool.
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.