  We introduce a new notion of stratification (``riso-stratification''), which
is canonical and which exists in a variety of settings, including different
topological fields like $\mathbb{C}$, $\mathbb{R}$ and $\mathbb{Q}_p$, and also
including different o-minimal structures on $\mathbb{R}$. Riso-stratifications
are defined directly in terms of a suitable notion of triviality along strata;
the key difficulty and main result is that the strata defined in this way are
``algebraic in nature'', i.e., definable in the corresponding first-order
language. As an example application, we show that local motivic Poincar\'e
series are, in some sense, trivial along the strata of the riso-stratification.
Behind the notion of riso-stratification lies a new invariant of singularities,
which we call the ``riso-tree'', and which captures, in a canonical way,
information that was contained in the non-canonical strata of a Lipschitz
stratification. On our way to the Poincar\'e series application, we show, among
others, that our notions interact well with motivic integration.
