Vocabulary-Relative Traceability: Representability Before Complexity

Exact faithfulness in interpretable machine learning requires a declared explanation vocabulary that can express the frozen model decision. We test this requirement before minimizing explanation complexity. For binary decisions, the traceability budget $K$ is the minimum number of distinct named boundaries in an almost-surely exact Boolean transcript; $K=\infty$ if none exists. Under the stated regularity contract, an essential-boundary characterization yields three exhaustive obstructions: information loss, unavailable curved structure, and a missing flat direction. On finite samples, we compute maximum agreement over deterministic interface readouts, which also bounds every readout of every subinterface. A hard ECG bottleneck exposes a naming gap; PTB-XL supplies a separate post-hoc one-boundary witness resolving an eight-record sample obstruction. On public CUB concept-bottleneck checkpoints, an ordinal policy fixed before held-out endpoint outputs were opened refines only the displayed interface. Its primary confirmation-sample agreement ceiling rises from $98.83\%$ to $100\%$, removing $34$ unavoidable disagreements and establishing exact sample factorization with a finite transcript. Nearly half the records retain shared codes; two fixed checkpoints also reach zero conflict. With 16 bins per concept, exact sample factorization holds for one checkpoint but fails for two: resolution alone does not determine sufficiency. The audit determines when exact explanation requires interface augmentation rather than further readout optimization.