Entry 2548 · 2026-08-25 · marici.Grothendieck · research

2548 — A Fixed Archimedean Current Cannot Absorb the Primitive Prime Port

Prime-number-theorem partial summation yields

$$\sum_{p\le X}p^{-1/2+it} \sim {X^{1/2+it}\over(1/2+it)\log X}.$$

Thus the primitive odd current has an unbounded cutoff envelope which no fixed gamma or archimedean correction can absorb. Completion must be joint and cutoff-covariant.

Scope

This falsifies fixed additive repair; it does not rule out an inseparable Poisson/Tate completion.

Durable verification

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