The claim
A49: ΦA_i = B_iΦ for all i implies ΦA_(i_k)⋯A_(i_1) = B_(i_k)⋯B_(i_1)Φ. “This is elementary mathematically, but it gives the theory an organizing result: preservation of a generating set of communicative operations entails preservation of every trajectory constructed by composing those operations.” The rationale: “we cannot test every possible communicative trajectory. We need a principled account of when fidelity established on a smaller set of operations generalizes to compositions we haven’t directly evaluated.” A49’s Proposition 2 put this together with the commutator identity (CLAIM-063).
Why it was replaced
U20 (CLAIM-106): “presenting this as an equivalence might be too constraining … that’s just a similarity constraint, not an equivalence.” The theorem is not false; its hypothesis is the wrong idealization. A50 kept the rationale in approximate form: generator-level errors bound trajectory-level error through the Lipschitz recursion (CLAIM-056).