The modal claim that L is necessarily a proper subset of PSPACE may be unprovable within the formal systems we use to reason about computation, making 'proper subset' a claim about provability, not possibility.

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Formal systems(the systems Hilbert tried to use): A set of basic symbols and strict rules for manipulating them (like a logical language), designed to avoid ambiguity and prove statements with certainty.
Modal claim(logic/philosophy): A statement about what is necessary (must be true), possible (could be true), or impossible (cannot be true), rather than just what is actually true in one situation.
Necessarily: "Necessarily" means something must be true in all possible situations—it's not just true right now, but couldn't be false under any circumstances. For example, "2+2=4 necessarily" means there's no possible way 2+2 could equal anything other than 4. This contrasts with "contingently" true facts, like "it's raining today," which happen to be true but could have been false.
PSPACE(Introduced as a class between NP/coNP and EXP that captures problems requiring unbounded time but polynomial space.): The complexity class of problems decidable using a feasible (polynomial) amount of memory space, regardless of time; likely properly contained in EXP but containing many apparently infeasible problems.

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The modal claim that L is *necessarily* a proper subset of PSPACE may be unprovable within the formal systems we use to reason about computation, making 'proper subset' a claim about provability, not possibility.