The triangulated Grothendieck group

K₀ of a triangulated category, its presentation by generators and three-term relations, and its functoriality in triangulated functors.

Nothing here mentions a slicing, a phase, or a stability condition. These modules lived under StabilityCondition/Foundation/ for historical reasons, which made every consumer of a Grothendieck group inherit the stability track as a dependency; they are generic triangulated theory and now sit where the subject hierarchy puts them.