  We set up a generalization of ubiquitous one parameter families in algebraic
geometry and its use for stability theories ([Mum65, HL14, AHLH23]) to families
over toric varieties, Novikov type rings, or its complex analytic analogues.
The language allows us to reformulate degenerations of "irrational" direction
in various literatures as canonical objects in a unified manner.
  Compatibly, we generalize the stable reduction type theorem for
$\Theta$-stratification in [AHLH23] of Langton type to our higher rank setup.
