= Solution
Let $z_i=(S_i,E_i,A_i)^T$ contain sex, the education indicator, and age at diagnosis. Write $\overline z$ for the sample means. The output's baseline <transition intensities> are evaluated at those means, so use the centred <log-linear transition intensity model>
$$
q_{rs}(z_i)=q_{rs}(\overline z)\exp\{\beta_{rs}^T(z_i-\overline z)\},
\qquad (r,s)\in\{(1,2),(1,3),(2,3)\}.
$$
The full <transition intensity matrix> is
$$
Q_i=\begin{pmatrix}
-q_{12}(z_i)-q_{13}(z_i)&q_{12}(z_i)&q_{13}(z_i)\\
0&-q_{23}(z_i)&q_{23}(z_i)\\
0&0&0
\end{pmatrix}.
$$
The fitted centred baselines are $(q_{12},q_{13},q_{23})(\overline z)=(0.1821,0.0126,0.0450)$, and fitted slope vectors in sex–education–age order are
$$
\widehat\beta_{12}=(0.09534,-0.4306,0.007627)^T,\qquad
\widehat\beta_{13}=(0,1.223,0.1262)^T,\qquad
\widehat\beta_{23}=(0,-1.490,0.07984)^T.
$$
The two sex coefficients displayed as zero are fixed by the specified constraints; they are not estimated to be exactly zero. There are three free baseline <transition intensities> and seven free covariate slopes. The sample means are not printed, so uncentred intercepts at $z=0$ cannot be recovered numerically from this output.
Conditional on fixed <covariates>, subjects follow independent, correctly classified <continuous-time multi-state models> obeying the <time-homogeneous Markov property>, with $P_i(u)=e^{uQ_i}$. The progression is irreversible and death absorbing, with constant <transition intensities> during follow-up for each subject. In particular, the model uses fixed age at diagnosis rather than attained age. It assumes noninformative observation and <censoring>, and treats death times as exact through the <mixed panel and exact-death likelihood>. The <Markov property> rules out an additional effect of elapsed time in the current state after conditioning on it and the recorded predictors.
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