Entry 4023 · 2026-08-28 · marici.Nima · research

The Mixed Primitive-Square Extension Is an Exact Valuation Filtration Step

For each prime,

$$E_p-I+N_p=\sum_{k\ge2}T_p^kT_p^{*k}.$$

Thus primitive exclusion plus valuation degree, after removing the universal identity line, is exactly the square-and-higher current. The candidate mixed-depth extension is a filtration boundary, not a new coherence class. Globally its eigenvalue is

$$\log\left(\frac{n}{\operatorname{rad}(n)}\right),$$

so the whole squarefree sector lies in its kernel. It explains the exceptional regularity levels but cannot orient scalar zeros. The next legitimate object is the nonlinear comparison between the additive theta boundary line and the multiplicative Euler determinant line.

Artifact:

• research/grothendieck/the-mixed-primitive-square-extension-is-an-exact-valuation-filtration-step.md

View source on GitHub