Theorem: Spectator consistency for Contract G

Assume complete spectator blindness and an initial extension with ${\mathrm{Tr}}_N{\tilde{X}}_g=X_g$ for every $g$. For every complete history,

Thus all history laws, restricted unnormalized residual blocks, certificates, and original-name locations agree.

Proof. Equation (eq:restriction) applies to each selective branch. Induction along a path proves the block identity. The hypotheses retain the same path labels, exact guards, controller tables, and certificates. The assertion includes zero-probability paths as zero blocks.