Fluid Sector Decomposition

The 4+1 template applied to fluid data. Each ω-germ decomposes into A/B/C/D-sector components. The ω-coupling mediates inter-sector energy transfer.

Fluid Sector Decomposition

Summary

The 4+1 template applied to fluid data. Each ω-germ decomposes into A/B/C/D-sector components. The ω-coupling mediates inter-sector energy transfer.

Statement

\label{def:fluid-sector-decomposition}
Let $f$ be $\tau$-admissible fluid data at primorial depth $n$. The \emph{fluid sector decomposition} of $f$ is the unique splitting
\begin{equation}
f \;=\; f_A + f_B + f_C + f_D + f_\omega,
\label{eq:ch35-fluid-sector-decomposition}
\end{equation}
where $f_S$ denotes the $S$-sector projection of $f$ for $S \in \{A, B, C, D, \omega\}$, obtained by restricting the spectral content of $f$ to the characters in $\operatorname{Sector}(S) \subseteq \operatorname{Char}(\mathbb{L})$.

The four primitive projections $f_A, f_B, f_C, f_D$ capture the flow components governed by the generators $\pi, \gamma, \eta, \alpha$ respectively. The coupling projection $f_\omega$ captures the inter-sector transfer mediated by the crossing generator $\omega$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-03.jsonl line 91
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch35-fluid-sectors-and-the-defect-functional.tex lines 40-51

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Physics.FluidData
• Name: abcd_check

Dependencies

• Canonical: III.D13, III.D14, III.D36

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.