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Totient counting asymptotic reference
Family 024: An asymptotic formula for the number of totients. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Arithmetic database researchers can compare distinct totient counts to a phase-dependent asymptotic equivalent.
Applicability and commercial boundary
The bounded factor is not a constant, and convergent arithmetic approximations may be expensive. No efficient inverse-totient enumerator follows.
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
Inspect computable factor approximation cost and finite error.
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.