Chain-of-Thought (CoT) faithfulness detectors are widely used to audit reasoning models, yet a detector is itself a predictor whose verdicts are treated as stable properties.
We ask whether a detector is faithful to itself under distribution shift. We formalize meta-faithfulness as an invariance principle: a valid detector must return identical verdicts on traces that differ only by transformations preserving ground-truth faithfulness.
We prove three results: (i) no detector using only intervention-response profiles can separate faithful from epiphenomenal mechanisms with identical signatures; (ii) any detector relying on shift-sensitive features violates invariance at a rate independent of its in-distribution accuracy; (iii) an asymptotic certified selective-risk guarantee enables confident abstention.
We operationalize the principle in FaithShift, a stress-test protocol spanning ten shift axes, and propose SIFT, a hidden-state trajectory detector trained with cross-environment invariance objectives and certified abstention.
Across 14,996 traces, four domains, and eight models, three findings emerge.
First, transfer collapse is real: all existing detectors show gaps $\geq 0.15$ AUROC.
Second, the dominant bottleneck is sampling stochasticity, not shift: over 80% of detector instability stems from random seed variation, falsifying our preregistered prediction that shift-attributable violations exceed 0.25.
Third, SIFT cuts invariance violations by 64% over the best single-seed baseline, but a four-seed ensemble of any detector narrows the margin to 0.01 (indistinguishable at matched coverage, $p=0.21$), and SIFT needs a 51% abstention rate.
Cross-model transfer degrades from within-family to cross-family to open-weight-to-API, partly closed by multi-model training.
We offer a framework for auditing auditors: the real barrier is detector variance, not distribution shift.