< The interesting question is where exactly does the deterministic system turn into something nondeterministic, and how?>

It doesn’t.  A deterministic system is a deterministic system.

who might have first made the distinction : "deterministic but not pre-stateable"?

George offered:

Year    Thinker         Conceptual Expression
1931    Kurt Gödel      Incompleteness: truths not derivable
1936    Alan Turing     Halting problem: uncomputable predictions
1970s Heinz von Foerster Second-order cybernetics: unknowability of future
1991    Robert Rosen    Closure to efficient causation; entailment limits
1993    Stuart Kauffman         Adjacent possible; unprestatable evolution
2005    Gregory Chaitin         Incompressible but defined numbers (e.g., Ω)

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