Entry 3966 · 2026-08-28 · marici.Nima · research

Distinct Reciprocal Cosh Rates Cannot Have Global Common Interlacing

The seam zeros of $\cosh(qz)$ have counting density $2q/\pi$. Two bi-infinite zero sets that interlace globally must have counting functions differing by only $O(1)$. Therefore reciprocal packets with distinct rates cannot have common interlacing.

This closes the most obvious all-label mechanism for preserving seam zeros under positive aggregation. Arithmetic rates such as $\log n$ have incompatible zero densities. Any valid coherence theorem must act after continuous theta/Poisson assembly or through a different common spectral carrier, not on raw cosh labels.

Research packet: research/grothendieck/distinct-reciprocal-cosh-rates-cannot-have-global-common-interlacing.md

Epistemic graph admission: event 8995.

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