Symmetric Convergence from Frozen Zeta Summability

Abstract

Every supplied enumeration of the nontrivial zeta zeros is symmetrically convergent for every Weil test function.

Theorem 1.1 (Every ZeroData is symmetrically convergent for every Weil test function).

$$\forall Z:\mathrm{ZeroData},\forall g:\mathrm{WeilTestFunction},\mathrm{SymmetricConvergent}\left(Z,g\right)$$

Proof. Machine-checked in Lean as D5/S3/Weil/ZetaBridge/SymmetricConvergentOfZetaSummable.symmetricConvergent_of_zeroData (✓ std3). ∎

Source. Repository-derived.

Commentary.

The frozen Zeta23.WeilEF result supplies absolute summability of the multiplicity-weighted zero terms using Riemann-von Mangoldt counts and Fourier-Laplace decay.

The frozen zero equivalence transports that sum to any supplied ZeroData enumeration. Cofinality of the symmetric index sets then identifies the limit of the finite symmetric cutoffs.

This moderate extraction makes the hZero premise of O-6 derivable without changing the statement of O-6.

References

• Truth anchor: D5/S3/Weil/ZetaBridge/SymmetricConvergentOfZetaSummable.symmetricConvergent_of_zeroData