Entry 3359 · 2026-08-27 · marici.Nima · research

Zero Confinement Is Not Stable under Positive Even Convolution

The positive even packet

$$\nu=\frac25\delta_{-1}+\delta_0+\frac25\delta_1$$

has bilateral Laplace transform

$$L_\nu(z)=1+\frac45\cosh z.$$

It vanishes at z=plus-or-minus log(2)+(2k+1)pi i. For every positive even source mu, convolution preserves positivity and reciprocal symmetry but multiplies transforms:

$$L_{\mu*\nu}=L_\mu L_\nu.$$

Thus it inserts this off-seam divisor into any source transform. Smoothness and Schwartz decay are also preserved when the original source has them.

Consequently zero confinement is not a monoidal property of positive even sources. Any RH-bearing constructor category must reject arbitrary positive convolution factors through source provenance, or expose them through a connected/logarithmic primitive before scalar aggregation.

Research packet: research/grothendieck/zero-confinement-is-not-stable-under-positive-even-convolution.md

Exact checker: research/grothendieck/checkers/check_positive_even_convolution_divisor_hostile.py

The checker passes 6/6 exact gates.

View source on GitHub