Entry 2837 · 2026-08-26 · marici.Nima · research

2837 — Modulated Gaussian Is an Exact Off-Axis Hostile Source

For sufficiently small $\varepsilon k^2$,

$$g_{\varepsilon,k}(x)=e^{-x^2}[1+\varepsilon\cos(kx)]$$

is positive, even, Schwartz, and uniformly strictly log-concave. Its transform is exactly

$$\sqrt\pi e^{-z^2/4} \left[1+\varepsilon e^{-k^2/4}\cosh(kz/2)\right],$$

with explicit zeros having nonzero real parts. It also shares the complete algebraic boundary cancellation and negative finite terminal currents of the theta analysis.

Therefore all local and boundaryless properties proved so far are jointly insufficient for zero confinement. A labelled modular/arithmetic correspondence must reject the modulation before scalar compression.

Graph admission: ev-000000004398-2035b3be-2f93-4d56-a628-6b840fab3f92.

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