%
\label{def:rewiring-table}
%   II.T06, II.T19, II.T25, II.T27, II.T30, II.T32, II.T39,
%   II.T40, II.D21, II.D22, II.D35, II.D60
The \textbf{rewiring table} is the twelve-level
structural comparison of orthodox ($i^2 = -1$)
and $\tau$ ($\jj^2 = +1$) mathematics,
refining the preview of
Section~\ref{sec:ch61-twelve-levels}
with explicit theorem references:

\medskip
\renewcommand{\arraystretch}{1.35}
\begin{center}
\begin{tabular}{@{}r@{\;\;}p{3.2cm}@{\;\;}p{3.2cm}@{\;\;}p{3.2cm}@{}}
\toprule
\textbf{\#}
  & \textbf{Orthodox ($i^2 = -1$)}
  & \textbf{$\tau$ ($\jj^2 = +1$)}
  & \textbf{Theorem source} \\
\midrule
1
  & $\mathbb{C}$ field, no ZD
  & $H_\tau$ ring, ZD
  & I.T10, I.D18 \\
2
  & Laplace $\Delta f = 0$
  & Wave $\Box f = 0$
  & II.D21, II.D22 \\
3
  & Interior glued by $\Delta$
  & Interior from boundary
  & I.T31, II.T27 \\
4
  & Unique $\omega$ absent
  & Unique $\omega$ (K2)
  & I.T36, II.D68 \\
5
  & $\aleph_0, \aleph_1, \ldots$
  & Single $\omega$, no hierarchy
  & I.T35, I.T36 \\
6
  & Archimedean, connected
  & Stone, ultrametric, clopen
  & II.T06, II.D13, II.D14 \\
7
  & Euclidean from axiom
  & Euclidean from theorem
  & II.T15--II.T18 \\
8
  & Compact $\Rightarrow$ constant
  & Compact + non-constant
  & II.T41 (Liouville dodge) \\
9
  & Fourier: $e_+ = e_-$ (harmonic)
  & Fourier: $e_+ \neq e_-$ (hol.)
  & II.T30, II.T32 \\
10
  & Liouville rigidity
  & Standing-wave flexibility
  & II.T40, II.T41 \\
11
  & Laurent $\to$ Cauchy
  & BndLift $\to$ CRT
  & II.D35, II.D36 \\
12
  & Spectrum at $\infty$ empty
  & $\omega$ spectral
  & I.D47, II.D60 \\
\bottomrule
\end{tabular}
\end{center}
\medskip
\noindent
Every entry in the table is backed by
a proved theorem or a registered definition
in Books~I--II.