THM0158canonicalv1Master Schema Theorem
All eight Millennium Problems are instances of Mutual Determination at varying enrichment levels: E₀ (RH, Poincaré — Part IV), E₁ (NS, YM, Hodge — Part V), E₁→E₂ (BSD, Langlands — Part VI), E₂ (P vs NP — Part VII). The spectral algebra provides the common language, the primorial ladder the common tower, the CRT the common local-global bridge.
Payload
Master Schema Theorem
All eight Millennium Problems are instances of Mutual Determination at varying enrichment levels: E₀ (RH, Poincaré — Part IV), E₁ (NS, YM, Hodge — Part V), E₁→E₂ (BSD, Langlands — Part VI), E₂ (P vs NP — Part VII). The spectral algebra provides the common language, the primorial ladder the common tower, the CRT the common local-global bridge.
Master Schema Theorem
Summary
All eight Millennium Problems are instances of Mutual Determination at varying enrichment levels: E₀ (RH, Poincaré — Part IV), E₁ (NS, YM, Hodge — Part V), E₁→E₂ (BSD, Langlands — Part VI), E₂ (P vs NP — Part VII). The spectral algebra provides the common language, the primorial ladder the common tower, the CRT the common local-global bridge.
Statement
\label{thm:master-schema}
All eight Millennium Problems are instances of Mutual Determination (Definition~III.D25) at varying enrichment levels:
\begin{itemize}
\item $E_0$ (spectral): RH, Poincar\'e (Part~IV).
\item $E_1$ (physics): Navier--Stokes, Yang--Mills, Hodge (Part~V).
\item $E_1 \to E_2$ (bridge): BSD, Langlands (Part~VI).
\item $E_2$ (computation): P~vs~NP (Part~IX).
\end{itemize}
The spectral algebra $A_{\mathrm{spec}}(\mathbb{L})$ provides the common language across all enrichment levels. The primorial ladder provides the common tower. The Chinese Remainder Theorem provides the common local-global bridge.
Proof / Justification
The proof is the content of Parts~IV through VI and~IX. Part~IV (this Part) establishes the pattern at $E_0$; subsequent Parts verify the details at progressively higher enrichment levels.
Source Context
- Registry source:
book-03.jsonlline 86 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part04/ch33-the-master-schema.texlines 186-195
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Doors.MasterSchema - Name:
master_schema_check
Dependencies
- Canonical: III.D25, III.T19, III.D35, III.P13
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.T23master-schema-theoremthm:master-schemaRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (5)
Appears in (1)
Downstream uses (computed) (10)
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Version & History
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