If the constructibility criterion is model-relative, the subset relation established by the Space Hierarchy Theorem inherits that relativity and cannot ground a model-independent claim about 'proper' containment.

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Constructibility criterion(mathematical and philosophical logic): A rule or standard for deciding what things are considered 'real' or 'valid' based on how they're built or constructed, rather than just assuming they exist on their own.
Inherits (in philosophical context)(logic and philosophy): Takes on or acquires the same qualities or properties as something else—like a child inheriting traits from a parent.
Proper containment(as used in mathematics and set theory): When one group is completely inside another group, but they're not the same size—like how all squares are rectangles, but not all rectangles are squares.
Space Hierarchy Theorem(as used in computational theory): A mathematical result in computer science that describes how problems of different difficulty levels can be organized based on how much computer memory they require to solve.
Subset relation(in formal logic): A mathematical relationship where one group is entirely contained within another—like how all squares are rectangles, but not all rectangles are squares.
model-independent(describing a type of measure): Not dependent on or limited to any one specific framework or system; true regardless of which particular model you're using.
model-relative(describing properties in logic and mathematics): Dependent on which particular version or interpretation of a system you're looking at; something can be true in one model but not in another.

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