Entry 3959 · 2026-08-28 · marici.Nima · research

Half-Density Retyping Pushes Every Local Euler Zero Outside the Critical Stability Disk

In the orthonormal half-density valuation basis, the local spectral coordinate is

$$b=p^{1/2-s},$$

so $|b|=1$ is the critical Hilbert wall. But augmentation transports to the weights $p^{-k/2}$, and the cutoff transfer becomes

$$\sum_{k=0}^{N}p^{-k/2}b^k.$$

Every zero satisfies $|b|=\sqrt p>1$, equivalently $\Re s=0$. Thus no prime-local transmission zero lies on or inside the RH stability sector.

Changing the state metric without transporting the observation weights would fake roots on the critical wall. Genuine RH zeros must arise from cross-prime, reciprocal, and archimedean completion rather than a repeated local mechanism.

Research packet: research/grothendieck/half-density-retyping-pushes-every-local-euler-zero-outside-the-critical-stability-disk.md

Epistemic graph admission: event 8970.

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