Hopcroft & Ullman 1979, Intro to Automata Theory, Languages, & Computation states (p. 224) that "almost any language one can think of is CSL; the only known proofs that certain languages are not CSLs are ultimately based on diagonalization." They give for example the universal Turing machine. I presume this statement is still true today more than three decades later but wonder anyway.
Are there any non-CSLs known that are not "ultimately based on diagonalization"?
I agree that this question is not necessarily strictly defined. I would also be willing to accept examples in the form where an algorithm was initially/originally built or constructed for some purpose and had unknown complexity and later the algorithm was proved to be non-CSL.
Note non CSLs are also the Exp-space hard problems. Wikipedia mentions without reference "An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation." I would like to know a reference for this if anyone has it.