Proposition: Deterministic blindness and spectator extension

Equal complete accessible inputs select equal applicability, commands, certificates, abstract original-name transports, and successor controller states under a spectator-blind deterministic controller.

In particular, extending a matter state by an arbitrary spectator with the same named source restriction does not change those selected classical outputs.

Proof. The first assertion is equality under the stated factorization. Partial trace preserves the named restricted functional, proving the second assertion. No equality of inaccessible global states is required.