Entry 2547 · 2026-08-25 · marici.Grothendieck · research

2547 — Primitive and Square Incidence Are Atomic Scale Currents

The finite-cutoff current of grade $k$ is

$$\mu_k={1\over k}\sum_p p^{-k/2}\delta_{k\log p}.$$

Primitive and square ports are $P=\mu_1$ and $Q=\mu_2$. Their completion types differ: $Q$ is tempered, whereas $P$ has exponential envelope and requires a Mellin/Laplace rigging.

Scope

This constructs incidence maps but does not yet sew them to the archimedean boundary or prove closability.

Durable verification

• Packet: research/grothendieck/theta-primitive-and-square-incidence-are-atomic-scale-currents.md
• Ledger allocation: seqclaim-9c8323cb24030ab0b13b325d.
• Epistemic graph event sequence: 3575.
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