THM0164canonicalv1Physics 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.jsonlline 116 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch43-the-physics-layer-complete.texlines 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
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
III.T29physics-layer-assemblythm:physics-layer-assemblyRelease lines
corpus_v3_workingcorpus_v2Relations
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.
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FTH0683formal theorem
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FTH0684formal theorem
FTH0684formal theoremSources
Version & History
Status disclaimer
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