Hodge Requires E₁

At E₀, all characters are NF-addressable (Book II Central Theorem). The Hodge question becomes non-trivial only at E₁, where sector admissibility predicates distinguish addressable-within-sector from addressable-globally.

Hodge Requires E₁

Summary

At E₀, all characters are NF-addressable (Book II Central Theorem). The Hodge question becomes non-trivial only at E₁, where sector admissibility predicates distinguish addressable-within-sector from addressable-globally.

Statement

\label{prop:hodge-requires-e1}
At enrichment level~$E_0$, every boundary character $\chi \in \operatorname{Char}(\mathbb{L})$ is globally NF-addressable. The Hodge question---which characters are sector-addressable---becomes non-trivial only at~$E_1$, where the $4{+}1$ sector decomposition introduces sector-specific admissibility predicates that are not present at~$E_0$.

Proof / Justification

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

Source Context

• Registry source: book-03.jsonl line 112
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch41-sigma-fixed-characters-and-sector-addressability.tex lines 115-119

Lean / Formalization Notes

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

Dependencies

• Canonical: III.T14, III.D13

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.