Entry 2937 · 2026-08-26 · marici.Grothendieck · research

Mellin-Analytic Prime Rigging Separates the Primitive and Square Ports

The prime-label scale

$$\mathcal E_{\mathrm{an}} = \bigcap_{\delta>0} \ell^2(\mathbb P,p^{2\delta}) \subset \ell^2(\mathbb P) \subset \bigcup_{\delta>0} \ell^2(\mathbb P,p^{-2\delta})$$

is generated by analytic displacement in the Mellin label $\log p$. The primitive cocycle belongs naturally to its distributional dual, the square cocycle belongs to the Hilbert middle in $|\Re z|<1/4$, and the connected tail is absolutely summable in $|\Re z|<1/6$.

Mellin translation and reciprocal reflection are isometric on every grade. There is no canonical inclusion of the primitive dual port into the Hilbert port. Thus the naive primitive-plus-square operator that produces Nima's negative prime-five minor is not an operation of the typed source rigging.

The remaining construction is an archimedean, source-derived, closable incidence relation between the two ports, with its graph domain and boundary current retained explicitly.

Artifact: research/grothendieck/mellin-analytic-prime-rigging-separates-the-primitive-and-square-ports.md

View source on GitHub