If no physical process can distinguish between two target system states, they constitute one physical state for all scientific purposes, potentially equalizing model and target cardinalities.

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Model and target cardinalities(in philosophy of science and formal ontology): The number of distinct things in a scientific theory (model) versus the number of distinct things in the real world (target); equalizing them means the theory and reality have the same count of different states.
Physical process(in philosophy of science and metaphysics): Any measurable change or interaction in the material world that follows the laws of physics—like heat transfer, motion, or chemical reactions.
Physical state(in philosophy of physics): The actual condition of something in the real world—for example, where an object is located and how fast it's moving.
Target system(as used in philosophy of science): The real-world thing you're trying to understand or study, as opposed to a simplified version of it.

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