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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 -stratification in AHLH23 of Langton type to our higher rank setup.
Yuji Odaka (Tue,) studied this question.
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