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Inhomogeneous approximation assumption reference
Family 022: The weak inhomogeneous Duffin–Schaeffer conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Researchers can organize almost-everywhere approximation under the stated divergent totient-weighted sum.
Applicability and commercial boundary
The claim is almost everywhere, has unrestricted numerators and no finite convergence rate; it does not guarantee a chosen real input or denominator budget.
Initial business decision
Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.
Next verification action
Identify an effective deterministic subclass before software approximation claims.
Evidence scope
The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.