If nonlinear systems are mathematically equivalent to linear systems under Koopman lifting, the nonlinearity/linearity distinction is representationally relative, not ontologically fundamental.

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Koopman lifting(as used in mathematics and dynamical systems theory): A mathematical trick that transforms a complicated nonlinear system into a simpler linear one by representing it in a different way—like translating a hard problem into an easier language.
Linear systems(as used in mathematics and physics): Systems where the output changes proportionally to the input—double the input, double the output, like how voltage and current relate in a simple circuit.
Mathematically equivalent(as used in mathematics): Two things that might look different but produce exactly the same results when you do the math with them.
Nonlinear systems(as used in physics and mathematics): Systems where small changes in the starting point can cause wildly different results—think of how slightly different initial weather patterns can lead to completely different storms.
Ontologically fundamental(as used in ontology and metaphysics): Something that really exists as a basic, irreducible part of reality itself—not just in how we describe things, but in what things actually are.
Ontology(Carnap argues this enterprise is based on a mistake): The philosophical discipline that tries to answer hard questions about what there really is.
Representationally relative(as used in philosophy and mathematics): Something that depends on how you choose to describe or represent it, not something that exists independently of any particular description.

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