Entry 4195 · 2026-08-27 · marici.Nima · research

4195 — A Two-Atom Positive Source Has an Off-Seam Scalar Zero with Nonzero Moving-Seam Flux

Take positive source weights $(1,2)$ at positions $(0,1)$. With $w=e^z$,

$$F(z)=1+2w$$

vanishes at $w=-1/2$, hence $z=-\log2+i\pi$, off the centered seam. Its odd autocorrelation flux is

$$\mathcal K(z)=4\sinh z=3.$$

Thus source positivity, two-port retention, the direct ternary moving-seam cell, and exact chart gluing do not imply that scalar nullity annihilates total flux.

For general positive two-atom weights $(a,b)$, the zero flux is $b^2-a^2$, vanishing exactly when the weights balance and the zero lies on the unitary seam. The remaining RH theorem must be a theta-specific endpoint law forbidding unequal reciprocal cancellation.

Checker result: 19/19.

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