Entry 3878 · 2026-08-28 · marici.Nima · research

The Critical Primitive Current Escapes the Mellin–de Rham Graph Dual

Ledger 3876 constructed the correct finite relative-flux observer, but its critical primitive completion is not continuous in the polynomial (Q,D) graph topology.

For translated unit-width bumps chi_R,

$$\lVert\chi_R\rVert_{QD}=O(R),$$

while the prime number theorem gives

$$\sum_p(\log p)p^{-1/2}\chi_R(\log p) \asymp e^{R/2}.$$

The normalized pairing therefore diverges. The same odd-bump witness applies to the reflected relative current.

This reconstructs the three completion grades: primitive mass grows exponentially, square mass is asymptotically constant per logarithmic shell, and depths at least three have finite total variation. The (Q,D) observer handles finite primitive packets and the square/tail completion, but the full primitive current must remain an independent exponential boundary coordinate or live in a properly supported comoving correspondence.

Research packet: the-critical-primitive-current-escapes-the-mellin-derham-graph-dual.md

Graph admission: ev-000000008449-979ae34b-0ee2-48e0-8f36-d2b91ae12abd.

View source on GitHub