NF-Addressability Theorem

Every σ-fixed boundary character at finite primorial depth is NF-addressable in every primitive sector. Proof by sector-by-sector verification (EM model case, then strong, weak, gravity).

NF-Addressability Theorem

Summary

Every σ-fixed boundary character at finite primorial depth is NF-addressable in every primitive sector. Proof by sector-by-sector verification (EM model case, then strong, weak, gravity).

Statement

%
\label{thm:nf-addressability}
Let $\chi \in \Char(\Lemniscate)$
be a $\sigma$-fixed boundary character
at finite primorial depth~$k$.
Then for every primitive sector
$S \in \{A, B, C, D\}$,
the $S$-projection $\pi_S(\chi)$
is NF-addressable.
More precisely:
there exists a primorial depth
$k_S \leq k$ such that
\begin{equation}\label{eq:ch42-nf-addressability}
    \operatorname{NF}\bigl(\pi_S(\chi)\bigr)
    \;=\;
    \operatorname{NF}\bigl(\pi_S(\chi)\big|_{\operatorname{Prim}(k_S)}\bigr),
\end{equation}
i.e., the normal-form extraction of the $S$-projection
stabilizes at depth~$k_S$
and carries no further information
at deeper primorial levels.

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

• Registry source: book-03.jsonl line 113
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch42-the-nf-addressability-theorem.tex lines 102-124

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Physics.Hodge
• Name: nf_addressability_check

Dependencies

• Canonical: III.D47, III.D48, III.T14, III.T13, III.D23

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.