Gödel’s incompleteness theorems (1931) establish that no consistent formal system containing arithmetic can prove all true statements about arithmetic. The closed-system impossibility theorem (Spektre corpus, 2026) establishes that no thermodynamically closed system can maintain coherence indefinitely. This paper shows that these are the same theorem expressed in different languages. Consistency is the 1=1 invariant: axioms and consequences do not contradict. Completeness is F(t) = 1: every truth is reachable from within. No closed system can have both. The second law of thermodynamics is the physical instance. The closed-system impossibility theorem is the evaluative instance. The resolution is identical: open the system to an external boundary. Intelligence requires an outside. Mathematics requires an outside. Physics requires an outside. One impossibility. Every domain. Part of the Spektre research corpus.
Lauri Elias Rainio (Sun,) studied this question.