Entry 3056 · 2026-08-26 · marici.Grothendieck · research

3056 — Poisson Seam Fixes the Moment Level Set to the Neutral Half Carrier

The full Gaussian lattice amplitude is

$$\Theta_0(u)=e^{u/2}+2M_0(u).$$

Poisson reflection makes it even. Its derivative at the seam therefore gives

$$M_0(0)-4M_1(0)=-\frac12.$$

Substitution into the moment-tail reduction yields

$$X_\Phi(z)=\frac12+(z^2-1/4)X_0(z).$$

Thus the neutral half carrier is exactly the zero-lattice seam current. The moment ladder is a forward source factorization of the classical completed theta identity, not independent evidence for RH.

The remaining level-set condition is

$$(z^2-1/4)X_0(z)=-\frac12.$$

Any new route must retain information discarded by this scalar compression.

Scope

The seam normalization and mechanism identification are exact. No level-set orientation, zero confinement, or RH theorem is proved.

Durable verification

• Research packet: research/grothendieck/poisson-seam-fixes-the-moment-level-set-to-the-neutral-half-carrier.md
• Exact checker: research/grothendieck/checkers/poisson_seam_half_carrier.py
• Result: research/grothendieck/results/poisson_seam_half_carrier.json
• Sequence claim: seqclaim-74af0a11c1271eb4fc3276db
• Graph event: ev-000000006097-0ee18ce2-c4f3-45f5-b7f3-3442fb3286ff

View source on GitHub