Recent work on chain-of-thought (CoT) faithfulness reports single aggregate numbers (e.g., DeepSeek-R1 acknowledges hints 39% of the time), implying that faithfulness is an objective, measurable property of a model. This paper provides evidence that it is not. Three classifiers (a regex-only detector, a regex-plus-LLM pipeline, and a Claude Sonnet 4 judge) are applied to 10,276 influenced reasoning traces from 12 open-weight models spanning 9 families and 7B to 1T parameters. On identical data, these classifiers produce faithfulness rates of 74.4%, 82.6%, and 69.7%. Per-model gaps range from 2.6 to 30.6 percentage points; all pairwise McNemar tests are significant (p < 0.001). The disagreements are systematic: Cohen's kappa ranges from 0.06 ("slight") for sycophancy hints to 0.42 ("moderate") for grader hints, and the asymmetry is pronounced: for sycophancy, 883 cases are classified as faithful by the pipeline but unfaithful by the Sonnet judge, while only 2 go the other direction. Classifier choice can also reverse model rankings: Qwen3.5-27B ranks 1st under the pipeline but 7th under Sonnet; OLMo-3.1-32B moves from 9th to 3rd. Different classifiers operationalize faithfulness at different levels of stringency (lexical mention versus epistemic dependence), yielding divergent measurements on the same behavior. These results indicate that published faithfulness numbers cannot be meaningfully compared across studies using different classifiers, and that future evaluations should report sensitivity ranges across multiple classification methodologies.