Assumption: Deterministic spectator-blind specification

For a fixed source embedding, the complete update specification is a deterministic function of

and any additional explicitly declared accessible inputs.

Equal such inputs select the same rule, guard result, support, proposed geometry, evaluated packet, certificate presentation, successor controller state, and transport of original names. They also select the same declared matter channel whenever a matter channel is included.

Every used record, seed, program counter, permission bit, resource test, and observable is part of that declared specification. Undeclared state descriptions and remote scheduler inputs are excluded.

Adding inaccessible spectators leaves the original label dictionary and all original input interpretations unchanged. Matter maps extend by the spectator identity, and accessible observables extend by $B\mapsto B\otimes I_N$. Geometric and coupling reservations are independent of spectator number. Spectator transport and history storage are reserved separately; their outcomes and capacity tests are not additional source inputs.