Archimedean-Elliptic Engine

The mechanism generating the orthodox SCV dimensional ladder: interaction of Archimedean metric dimension (continuous manifold with free parameter n) and elliptic CR overdeterminacy (n(n-1)/2 integrability conditions beyond n basic equations). Requires BOTH ingredients; neither alone generates a ladder.

Archimedean-Elliptic Engine

Summary

The mechanism generating the orthodox SCV dimensional ladder: interaction of Archimedean metric dimension (continuous manifold with free parameter n) and elliptic CR overdeterminacy (n(n-1)/2 integrability conditions beyond n basic equations). Requires BOTH ingredients; neither alone generates a ladder.

Statement

%
\label{def:archimedean-elliptic-engine}
The \textbf{Archimedean-Elliptic Engine} (AEE)
is the combination of two properties:
\begin{enumerate}
    \item[\textup{(A)}]
          \textbf{Archimedean density:}
          between any two distinct points
          lie uncountably many others.
          Limits refine without bound.
    \item[\textup{(E)}]
          \textbf{Elliptic regularity:}
          the Laplace equation $\Delta f = 0$
          forces holomorphic functions
          to be infinitely differentiable,
          with convergent power series
          at every point.
\end{enumerate}
The AEE is present in orthodox $\mathbb{C}^n$
and absent in $\tau^3$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-02.jsonl line 189
• Manuscript source: 2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part11/ch63-refuses.tex lines 250-271

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookII.Mirror.DimensionalLadder
• Name: ArchimedeanEllipticEngine

Dependencies

• Canonical: II.D73, II.D68

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.