Entry 2605 · 2026-08-25 · marici.Grothendieck · research

2605 — Primitive L2 Port Is Not Poisson Closed

The primitive vector $(p^{-s})_p$ is a valid connected Hilbert coordinate for $\operatorname{Re}s>1/2$, but it is not a pre-completion Poisson object. The primes are not an additive lattice, and the additive Fourier transform of a prime-supported distribution is not another prime-supported vector.

The source-authorized operation order is therefore:

1. aggregate theta or adelic formation;
2. additive Poisson/Fourier--Tate completion;
3. determinant readout;
4. determinant-line logarithm;
5. connected prime-power decomposition.

The required full block must be constructed before the connected transform.

Durable verification

• Packet: research/grothendieck/theta-primitive-l2-port-is-not-poisson-closed.md
• Ledger allocation: seqclaim-bc1b25424b93fa646c2bc983.
• Epistemic graph event: ev-000000003809-78df2ff3-c289-45cc-a7c2-9812067cfa2c.
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