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> There is nothing stopping inductively increasing the size of the input context and the number of entries in the ground truth table arbitrarily

This isn’t induction. You’ve only done the base case, not the induction hypothesis or induction step. Maybe you’ve done those steps in your head but that’s not really a trivial proof as you claim.

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Induction is "if this is possible for value X, then it is also possible for value X+1".

Where X isn't used as part of the step this is always true. Nothing I did depends on the size of either the input nor the truth table, so long as both are finite-size and so long as the truth table can be expressed as a function of the input.

An LLM is an arbitrary convolution of the input text; for any mapping, some function you can call an "LLM" produces that function.

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