  We provide a data mine of proven results for multiple zeta values (MZVs) of
the form $\zeta(s_1,s_2,...,s_k)=\sum_{n_1>n_2>...>n_k>0}^\infty \{1/(n_1^{s_1}
>... n_k^{s_k})\}$ with weight $w=\sum_{i=1}^k s_i$ and depth $k$ and for Euler
sums of the form $\sum_{n_1>n_2>...>n_k>0}^\infty t\{(\epsilon_1^{n_1}
>...\epsilon_1 ^{n_k})/ (n_1^{s_1} ... n_k^{s_k}) \}$ with signs
$\epsilon_i=\pm1$. Notably, we achieve explicit proven reductions of all MZVs
with weights $w\le22$, and all Euler sums with weights $w\le12$, to bases whose
dimensions, bigraded by weight and depth, have sizes in precise agreement with
the Broadhurst--Kreimer and Broadhurst conjectures. Moreover, we lend further
support to these conjectures by studying even greater weights ($w\le30$), using
modular arithmetic. To obtain these results we derive a new type of relation
for Euler sums, the Generalized Doubling Relations. We elucidate the "pushdown"
mechanism, whereby the ornate enumeration of primitive MZVs, by weight and
depth, is reconciled with the far simpler enumeration of primitive Euler sums.
There is some evidence that this pushdown mechanism finds its origin in
doubling relations. We hope that our data mine, obtained by exploiting the
unique power of the computer algebra language {\sc form}, will enable the study
of many more such consequences of the double-shuffle algebra of MZVs, and their
Euler cousins, which are already the subject of keen interest, to practitioners
of quantum field theory, and to mathematicians alike.
