Non-Emptiness Theorem

Each enrichment layer E_k (k = 0,1,2,3) is inhabited: it contains genuine objects and morphisms. Constructive witnesses: E₀ = any τ-object with NF address, E₁ = H_τ-enriched Hom spaces, E₂ = proto-codes from BSD carriers (preview), E₃ = self-modeling codes (preview).

Non-Emptiness Theorem

Summary

Each enrichment layer E_k (k = 0,1,2,3) is inhabited: it contains genuine objects and morphisms. Constructive witnesses: E₀ = any τ-object with NF address, E₁ = H_τ-enriched Hom spaces, E₂ = proto-codes from BSD carriers (preview), E₃ = self-modeling codes (preview).

Statement

%
\label{thm:non-emptiness}
Each layer of the enrichment tower is inhabited:
\begin{enumerate}
    \item $E_0$ is non-empty.
          Witness: any $\tau$-object with NF address.
    \item $E_1$ is non-empty.
          Witness: $[A, B]$ for $A, B$ in distinct spectral sectors.
    \item $E_2$ is non-empty.
          Witness: a proto-code from the BSD rational bridge
          (Part~VI).
    \item $E_3$ is non-empty.
          Witness: a self-modelling code
          with consistent interpretation functor
          (Book~VII).
\end{enumerate}
Items~(1) and~(2) are proved constructively
from Books~I--II structures.
Items~(3) and~(4) carry precise forward references.

Proof / Justification

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

Source Context

• Registry source: book-03.jsonl line 15
• Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part01/ch06-non-emptiness-and-strictness.tex lines 191-211

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookIII.Enrichment.CanonicalLadder
• Name: non_emptiness_8_3

Dependencies

• Canonical: III.D05, III.D06, III.D07, III.D08, III.D09

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.