If computational complexity classes are model-relative rather than model-invariant, the 'proper containment' of L in PSPACE may reflect artifact of the Turing formalism rather than an absolute mathematical fact.
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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.
Turing formalism(as used in computer science and mathematical logic)
The basic mathematical rules and symbols that computer scientist Alan Turing created to precisely define what 'computation' and 'solving a problem' actually mean.
artifact(Contrasted with real cellular structures in evaluating microscopy results)
A feature in a micrograph produced by the methods of preparation rather than by actual structures in the cell
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.