Theoretical analysis demonstrates computational universality in universal physical substrates, indicating that physical systems cannot contain a complete self-description.
The substrate of the universe is computationally universal — it can, in principle, simulate any computation. This is not just a philosophical claim but a theorem derived in the GTE framework: the GTE polynomial, via its invariant Rule 110 sub-automaton, is Turing-complete (machine-certified in Lean 4, zero sorry). Computational universality has profound consequences: any sufficiently rich physical system is subject to undecidability and Godel incompleteness. This tutorial explains what computational universality means for physics, how Turing completeness is established for the GTE substrate, and why it implies that the universe cannot have a complete self-description within itself — a result directly connected to the PSC (Perfect Self-Containment) principle and to the Transputation theorem placing quantum measurement at Turing degree 0'.
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Nova Spivack (2026) studied this question.
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