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Cubic Gauss sum exact reference library
Family 023: Patterson's first moment for cubic Gauss sums. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Analytic-number-theory researchers can compare the explicit first moment and angular-mode behavior over primary Eisenstein primes.
Applicability and commercial boundary
All-primary sampling, both conjugates and asymptotic error terms matter. This does not improve generic FFT or signal modulation without a separate computational bridge.
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
Extract the main coefficient and exact finite sum implementation.
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.