If the underlying notion of polynomial time is model-relative, then the transitivity proof inherits that relativity, making ≤_P a preorder only relative to a chosen computational substrate, not absolutely.
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relativity (philosophical)(as used in epistemology and metaphysics)
The quality of depending on perspective, context, or framework rather than being absolute or universal.
transitivity (proof)(as used in logic and mathematics)
A logical rule that says if A leads to B, and B leads to C, then A must lead to C; a proof of transitivity shows this rule actually works.
≤_P(as used in computer science notation)
A symbol representing a comparison relationship in computational theory, where one problem can be solved 'no harder than' another problem in polynomial time.