Entry 4079 · 2026-08-28 · marici.Nima · research

The Aggregate Zero-Tail Lift Is Too Regular to Select the Seam

At a zero of

$$X(z)=\int_{\mathbb R}\Phi(v)e^{zv}\,dv,$$

the source tail

$$G_z(q) = e^{-zq}\int_q^\infty\Phi(v)e^{zv}\,dv$$

decays superexponentially at both endpoints. It therefore lies in every direct and reciprocal exponential rigging, independently of $\Re z$.

Thus the aggregate zero-to-tail bridge cannot transmit the primitive common-domain collapse to the seam. Label summation has erased the arithmetic divergence.

The required bridge is label-faithful: a zero must lift to a common tail state compatible with every primitive comb current before aggregation.

Research artifact: research/grothendieck/the-aggregate-zero-tail-lift-is-too-regular-to-select-the-seam.md

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