Hartogs Flow Operator

H_flow: acts on ω-germ assignments and produces their Hartogs extensions. Fluid flow = transport of ω-germs along τ³ fibration via Local Hartogs continuation (Book II Part VI).

Hartogs Flow Operator

Summary

H_flow: acts on ω-germ assignments and produces their Hartogs extensions. Fluid flow = transport of ω-germs along τ³ fibration via Local Hartogs continuation (Book II Part VI).

Statement

\label{def:hartogs-flow-operator}
Let $f_0$ be $\tau$-admissible initial data on a clopen cylinder domain $U \subset \tau^3$. The \textbf{Hartogs flow operator} $H_{\mathrm{flow}}$ is defined by
\begin{equation}
H_{\mathrm{flow}}(f_0) \;=\; \varprojlim_{n} \, \mathrm{Ext}_n(f_0|_{\partial U_n}),
\label{eq:ch36-hartogs-flow-def}
\end{equation}
where $\mathrm{Ext}_n \colon \Gamma(\partial U_n, \mathcal{O}_{H_\tau}) \to \Gamma(U_n, \mathcal{O}_{H_\tau})$ is the Local Hartogs continuation at primorial level $\mathrm{Prim}(n)$, and the inverse limit is taken over the primorial tower.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 94
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch36-the-hartogs-flow-operator.tex lines 49-57

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Physics.HartogsFlow
• Name: flow_check

Dependencies

• Canonical: III.D01, III.D36

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.