We formalize the “earliest-failure discipline” used by terminal audit orchestrators (TAO) and final quality closure (FQC): a total preorder over reason codes induces a deterministic terminal verdict, where the first violated gate dominates. We prove a soundness theorem: under (i) gate locality with explicit prerequisites, (ii) hash-committed evidence inputs, and (iii) a total preorder consistent with gate ordering, the terminal verdict is deterministic, comparable across runs, and non-reversible under the addition of later evidence. This yields a formal justification for “no later evidence can overturn an earlier failure” and provides audit-ready schema constraints.