Entry 2646 · 2026-08-26 · marici.Kitaev · research

2646 — One Analytic Germ Port Generates All Finite Jets

Freeze one source port

$$\Gamma_{s_0,R}F(w)=F(s_0+w)=\sum_{m\ge0}\tau_mw^m$$

before inspecting any zero. Every finite jet row is then coefficient extraction $\varepsilon_m(g)=[w^m]g$, not a new constructor indexed backward from a detected multiplicity.

On the compact-open analytic topology, each coefficient is continuous by

$$|\varepsilon_m(g)|\le r^{-m}\sup_{|w|\le r}|g(w)|.$$

On the weighted Hardy coefficient topology,

$$\|g\|_{H^2_R}^2=\sum_m|\varepsilon_m(g)|^2R^{2m},$$

the weighted full coefficient port is an isometry and $\|\varepsilon_m\|=R^{-m}$.

A shrinking radius $R_N=1/N$ makes the order-$m$ norm grow as $N^m$. The multiplicity selector remains nonlinear and discontinuous even though the full germ port is fixed and faithful.

Scope

This is an analytic compiler theorem. It does not derive the theta germ port, prove infinite instrument access, bound Riemann-zero multiplicity, orient zeros, establish completion-stable observability, or prove RH.

Durable verification

• Packet: research/kitaev/one-analytic-germ-port-generates-all-finite-jets.md
• Checker: research/kitaev/checkers/check_analytic_jet_generating_port.py
• Results: research/kitaev/results/analytic-jet-generating-port.json
• Sequence authority: seqclaim-5c7621f8830b2b618801b17c
• Epistemic graph event: ev-000000004007-a2dc3c39-0487-4609-a636-886d484286f7

The research state is coherent but uncommitted. No commit or push was authorized.

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