Generated Golden Germ Zero Certificate

Abstract

The generated L2c certificate encloses all sixty-one modes at the frozen candidate, assembles the center norm and derivative margins, and closes the prime-two golden local-factor zero obligation.

The in-repo generator tools/scripts/agent/germ_jet_certificate.py emits this module deterministically; –check regenerates and byte-compares it. Its 61-row rational table has columns termReLo/Hi, termImLo/Hi, derivReLo/Hi, and derivImLo/Hi for v = 0,…,60. Exact assembly gives center real interval [-6.898169e-12,-6.8981e-12], center imaginary interval [2.75425869e-10,2.75425943e-10], additive norm bound 17645257/62500000000000000 = 2.82324112e-10, and derivative-real lower bound 1877338029556539187/10^18 = 1.877338029556539187.

Theorem 1.1 (The 61-mode truncation is smaller than four times 10^{-10}).

$$\Vert g\left(60,c\right)\Vert <\frac{4}{10^{10}}$$

Proof. Machine-checked in Lean as D5/S3/Analytic/GermWindow/GermZeroCertificate.g60_center_norm_lt (✓ std3). ∎

Source. Repository-derived.

Commentary.

The real and imaginary generated interval sums are converted by the frozen coordinate norm lemma. The certified 2.82324112e-10 bound lands below the preregistered 2.9e-10 falsifier threshold.

Theorem 1.2 (The derivative real part exceeds 1.87).

$$\frac{187}{100}<\Re \mathrm{deriv}\left(g\left(60\right),c\right)$$

Proof. Machine-checked in Lean as D5/S3/Analytic/GermWindow/GermZeroCertificate.g60_center_deriv_re_gt (✓ std3). ∎

Source. Repository-derived.

Commentary.

Summing the sixty-one exact derivative lower endpoints gives 1.877338029556539187, so the required strict 187/100 margin holds.

Theorem 1.3 (The prime-two golden local factor has a nearby zero).

$$\exists z\in \mathbb{C},z\in \mathrm{ball}\left(c,\frac{1}{10^8}\right)\wedge \mathrm{germLocalFactor}\left(z,2\right)=0$$

Proof. Machine-checked in Lean as D5/S3/Analytic/GermWindow/GermZeroCertificate.germLocalFactor_two_has_zero_near_candidate (✓ std3). ∎

Source. Repository-derived.

Commentary.

This bind-only closure combines the generated center norm and derivative bounds with the frozen L2a curvature theorem and the L1 center-jet reduction. It closes G-c: the p = 2 golden local factor has a zero within 10^{-8} of c approximately 0.23815 + 5.25671 i. This is the kernel refutation of addendum ten’s claim of no cancellation in the window. It says nothing about RH itself.

References

• Truth anchor: D5/S3/Analytic/GermWindow/GermZeroCertificate.g60_center_deriv_re_gt
• Truth anchor: D5/S3/Analytic/GermWindow/GermZeroCertificate.g60_center_norm_lt
• Truth anchor: D5/S3/Analytic/GermWindow/GermZeroCertificate.germLocalFactor_two_has_zero_near_candidate
• Dependency: D5/S3/Analytic/Certified/TrigEnvelopePhaseReduction
• Dependency: D5/S3/Analytic/GermWindow/GermJetModeLemma
• Dependency: D5/S3/Analytic/GermWindow/GermZeroCertificateJet
• Dependency: D5/S3/Analytic/GermWindow/GermZeroCertificateReduction