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\label{def:spine-address-path}
Let $X, Y \in \tau^3$ be two finite-stage points
with ABCD addresses
$(A_X, B_X, C_X, D_X)$
and $(A_Y, B_Y, C_Y, D_Y)$.
A \textbf{spine address path} from $X$ to~$Y$
is the pair of address chains:
\begin{enumerate}
    \item[\textbf{(i)}] \textbf{Descent.}
          $X \to \cdots \to \alpha_1$:
          the sequence of normal-form reductions
          obtained by successively stripping
          the ABCD coordinates of~$X$
          down to the base index $\alpha_1 = 2$
          (the first element of the $\alpha$-orbit).

    \item[\textbf{(ii)}] \textbf{Ascent.}
          $\alpha_1 \to \cdots \to Y$:
          the sequence of address reconstructions
          building up the ABCD coordinates of~$Y$
          from $\alpha_1$.
\end{enumerate}
The \textbf{spine address length} is
$\ell(X, Y) := \ell(X) + \ell(Y)$,
where $\ell(X)$ and $\ell(Y)$
are the number of greedy peel steps
in the descent from $X$ and $Y$
to~$\alpha_1$, respectively.