Radial-Solenoidal Split

Radial-Solenoidal Split

Radial-Solenoidal Split

Summary

Radial-Solenoidal Split

Statement

%
\label{def:radial-solenoidal}
The \textbf{radial--solenoidal split} of $\dim_\tau = 4$ is
\[
    \boxed{4 \;=\; \underbrace{1}_{\text{radial (D)}}
    \;+\;
    \underbrace{3}_{\text{solenoidal (A, B, C)}}.}
\]
The \textbf{radial} coordinate~$D$
measures depth in the primorial hierarchy ---
the remainder after peeling away the tower.
The \textbf{solenoidal} coordinates $A$, $B$, $C$
parametrize the tower
(leading prime, exponent, tetration height)
and wind around the primorial cycles.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-02.jsonl line 38
• Manuscript source: 2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part03/ch15-dimension-four.tex lines 229-245

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookII.Topology.DimensionFour
• Name: radial_solenoidal_check

Dependencies

• Canonical: II.T11

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.