Corpus theorem canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Theorem cid001621THM0164canonicalv1

Physics Layer Assembly

NS (mortar/regularity), YM (bricks/mass gap), Hodge (blueprint/addressability) together construct the E₁ enrichment layer. All three are instances of Mutual Determination at E₀→E₁.

Payload

Physics Layer Assembly

NS (mortar/regularity), YM (bricks/mass gap), Hodge (blueprint/addressability) together construct the E₁ enrichment layer. All three are instances of Mutual Determination at E₀→E₁.

Physics Layer Assembly

Summary

NS (mortar/regularity), YM (bricks/mass gap), Hodge (blueprint/addressability) together construct the E₁ enrichment layer. All three are instances of Mutual Determination at E₀→E₁.

Statement

\label{thm:physics-layer-assembly}
The three Part~V results---positive regularity (III.T25), the Yang--Mills gap (III.T27), and NF-addressability (III.T28)---are instances of Mutual Determination (Definition~\ref{def:mutual-determination-schema}) at enrichment level~$E_1$, with the following unified structure:

\begin{center}
\begin{adjustbox}{max width=0.95\linewidth}
\begin{tabular}{llll}
\toprule
\textbf{Problem} & \textbf{Boundary Data ($B$)} & \textbf{Spectral Structure ($S$)} & \textbf{Interior Consequence ($I$)} \\
\midrule
NS & $\tau$-admissible fluid data & Defect contractivity & Stabilized $\omega$-germ \\
 & (Def.~\ref{def:tau-admissible-fluid-data}) & $\Delta(f,n) \to 0$ & (regularity) \\
\addlinespace
YM & $\tau$-admissible gauge data & NF discreteness & Spectral gap \\
 & (Def.~\ref{def:tau-admissible-gauge-data}) & $|\operatorname{NF}| \le \operatorname{Prim}(k)$ & $\Gamma^*_s > 0$ \\
\addlinespace
Hodge & $\sigma$-fixed characters & Balanced $B/C$ content & NF-addressable \\
 & (Def.~\ref{def:sigma-fixed-character}) & $\chi_+ / \chi_-$ equilibrium & in all sectors \\
\bottomrule
\end{tabular}
\end{adjustbox}
\end{center}

\noindent In each case, the boundary data uniquely determines the spectral structure, which uniquely determines the interior consequence. The bidirectional passage $B \leftrightarrow S \leftrightarrow I$ closes because the interior consequence reconstructs the boundary data via the primorial tower maps.

Proof / Justification

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

Source Context

  • Registry source: book-03.jsonl line 116
  • Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch43-the-physics-layer-complete.tex lines 78-103

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookIII.Physics.PhysicsAssembly
  • Name: physics_assembly_check

Dependencies

  • Canonical: III.T25, III.T27, III.T28, III.D25

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001621
  • Primary alias THM0164
  • Type Theorem
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

III.T29physics-layer-assemblythm:physics-layer-assembly

Release lines

corpus_v3_workingcorpus_v2

Relations

Formalized by (5)

Appears in (1)

Downstream uses (computed) (10)

Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.

Sources

  • Monograph cid000024Book III, Part 5, Chapter 43 (Part V)

Version & History

  • v1 · 2026-05-10 imported from v2 registry
  • v1 · 2026-05-10 wired formalized by in wave 5

Status disclaimer

A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.

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