Incompleteness, Observation, and Spectral Truth: A Gödel-Consistent Theory of Everything and Its Fundamental Limits

This preprint unifies Gödel’s incompleteness theorems with quantum mechanics by introducing spectral truth, wherein propositions exist as superpositions of possible truth states and collapse into classical facts only upon observation. The framework formalizes this using axioms, lemmas, and proofs, deriving unavoidable limits on predictability, time, entropy, consciousness, and artificial general intelligence. Incompleteness is shown to be a necessary stability condition for any universe capable of observation and evolution, demonstrating that a complete Theory of Everything cannot exist as it would eliminate entropy, time, and freedom.

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