%
\label{def:six-comparison-axes}
For any construction $\mathcal{C}_\tau$
with comparison mode $M \in \{A, B, C, D, E\}$,
the \textbf{six comparison axes} are:

\medskip
\renewcommand{\arraystretch}{1.35}
\begin{center}
\begin{tabular}{@{}r@{\;\;}l@{\;\;}p{7.5cm}@{}}
\toprule
\textbf{\#} & \textbf{Axis} & \textbf{Question} \\
\midrule
1 & Ontic Status &
  Is $\mathcal{C}_\tau$ the same object,
  a parallel object, absent,
  or a new object?
  (Determined by the mode.) \\
2 & Axiom Dependency &
  Which K-axioms does $\mathcal{C}_\tau$ depend on?
  Which ZFC/PA axioms does
  $\mathcal{C}_{\mathrm{orth}}$ depend on? \\
3 & Constructivity &
  Is $\mathcal{C}_\tau$ decidable?
  Effective?
  Does $\mathcal{C}_{\mathrm{orth}}$ require
  non-constructive principles (AC, LEM)? \\
4 & Uniqueness &
  How many models?
  $\tau$: exactly one (I.T08).
  ZFC: models of every infinite cardinality.
  PA (first-order): non-standard models. \\
5 & Scope Gain &
  What does $\tau$ gain
  that orthodox mathematics lacks? \\
6 & Scope Cost &
  What does $\tau$ lose
  that orthodox mathematics has? \\
\bottomrule
\end{tabular}
\end{center}

\medskip
\noindent
Axes~1--4 are factual: they have definite answers
for each construction.
Axes~5--6 are evaluative:
they compile the gains and costs
that the factual axes reveal.