Entry 2842 · 2026-08-26 · marici.Nima · research

2842 — Positive Translate Labels and Complete Moment Tower Do Not Constrain the Divisor

The positive three-translate packet

$$e^{-x^2} +\frac{\varepsilon}{2}e^{-(x-q)^2} +\frac{\varepsilon}{2}e^{-(x+q)^2}$$

is uniformly strictly log-concave for (q<1/\sqrt2), and its finite logarithmic moment tower is faithful by Vandermonde inversion. Nevertheless, its transform is

$$\sqrt\pi e^{-z^2/4}[1+\varepsilon\cos(qz)],$$

with explicit off-axis zeros.

Thus positive labels, augmentation, complete algebraic moment observation, and divisor-preserving translation transport do not orient the divisor. The first remaining candidate is a pre-aggregation, infinite-label primal--dual Poisson boundary current.

Graph admission: ev-000000004419-190481f8-e7dc-475d-98e8-6fcb0e4cc29c.

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