This paper develops a first-principles calculus for classification-induced cognitive drift: situations in which a disclosed label, score, or classification output does not merely describe a target, but changes the target’s self-model, institutional treatment, evaluator commitments, downstream evidence, and later reclassification. The framework is designed for both human and AI settings in which classification is reflexive and deployment itself can reshape the system being measured. The manuscript models a classification regime as a hybrid controlled dynamical system with target, institution, evaluator, and classifier states, together with a discrete label plus continuous payload, split disclosure controls, contradiction-triggered revision, and authenticated classifier-state logging. A central contribution is the explicit separation of drift, distortion, and benefit, and the parallel separation of structural quantities from operational estimands. The paper introduces a four-level semantics ladder spanning exact replay with a canonical common-shock comparator, paired repeated-measures designs, staggered or panel rollouts, and matched or interference-limited observational comparisons. Outside exact replay or another declared canonical comparator, structural drift is treated conservatively as comparator-indexed rather than as an automatically intrinsic regime-level object. On the theory side, the paper provides a primitive chart-based route to local anchor-safety synthesis, dangerous-cell control results, high-probability audited recovery guarantees for declared projections, and deployment certificates that combine localization support, measurement validity, randomized live-sentinel evaluation, and an observable finite-signature transport envelope. On the measurement side, it clarifies when strong audit is possible, especially for classifier state, and when weaker observables support only decoded contrasts, bounded selected-audit scores, or local contradiction-cell booster estimands. On the deployment side, it supplies a conservative control language for deciding when induced drift is measurable, when hazardous states are controllable, and when rollout remains reversible, contestable, and worth the intervention risk. The paper is intended as a reusable theoretical foundation for researchers and practitioners working on reflexive classification, performative prediction, human–AI evaluation loops, decision support systems, algorithmic labeling, auditing, and deployment governance. It does not assume that classification is intrinsically harmful, and it does not claim full empirical identification of all latent quantities. Instead, it offers a conservative and machine-readable framework for distinguishing what is structural, what is measurable, what is only partially identified, and what must be certified before deployment.
K Takahashi (Sun,) studied this question.