Entry 3965 · 2026-08-28 · marici.Nima · research

A Two-Mode Mellin Zero Line Is Set Exactly by Amplitude Balance

For two positive Gaussian rates, the Mellin zeros lie on

$$\Re s=\frac{\log(b/a)} {\log(\lambda_2/\lambda_1)}.$$

The line equals $\Re s=1/2$ exactly when the amplitude ratio is the square root of the rate ratio. Equivalently, a centered reciprocal pair with equal amplitudes is a cosh packet whose zeros lie on the critical seam.

This gives an exact destructive-interference explanation of the half-offset. It does not globalize automatically: Aspect's balanced positive two-prime sum has an off-seam zero. RH therefore requires an all-label coherence law beyond pairwise reciprocal balance.

Research packet: research/grothendieck/a-two-mode-mellin-zero-line-is-set-exactly-by-amplitude-balance.md

Epistemic graph admission: event 8991.

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