Offline-Zero Reflection-Quotient Coordinate

Abstract

Reflection identifies the spectral quotient coordinate of an offline-zero parameter by an exact complex polynomial formula.

Definition 1.1 (The reflection quotient gives the exact offline-zero coordinate).

Lean statement: D5/S3/Weil/ZetaLinear/OfflineZeroSpectralQuotient.offline_zero_spectral_quotient_coordinate

Formalization. D5/S3/Weil/ZetaLinear/OfflineZeroSpectralQuotient.offline_zero_spectral_quotient_coordinate (✓ std3).

Source. Repository-derived.

Commentary.

The coordinate lambda(s) is defined as s times its existing functional reflection 1 - s, so the offline-zero parameter rho is shared with the preceding character construction.

Substituting rho = 1/2 + delta + i gamma gives real part 1/4 + gamma squared - delta squared and imaginary part -2 delta gamma.

The definition is realized concretely at delta = gamma = 1, where rho = 3/2 + i and lambda(rho) = 1/4 - 2i.

References

• Truth anchor: D5/S3/Weil/ZetaLinear/OfflineZeroSpectralQuotient.offline_zero_spectral_quotient_coordinate
• Dependency: D5/S3/Weil/ZetaLinear/OfflineZeroCharacter