ℓPart 2· Theorem C

Theorem C — Self-Interpretation

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Prerequisites: Theorem B (door finiteness), Chapter 6 (Axiom A5).

Theorem C. Under Axiom A5, $Σ_{τ} (F, t)$ and $e (F, t)$ are determined by $D (F, t)$ alone.

Proof. (Complete; reproduced from Chapter 6.)

$b_{F, t} (i) = d_{t} (i) - \sum_{j \in F} W_{t} (i, j)$ . Both terms are in $D (F, t)$ . $Σ_{τ}$ is a level set; $e_{p} = b_{F, t} (p)$ . No exterior information is used. $□$