Data systems operating under persistent legal, institutional, and analytic disagreement require shared reference without presupposing agreement about interpretation. This paper investigates identity preservation under transformation, building on the conditional neutrality result of Neutral Substrates (arXiv:2601.14271). We pair candidate identity bases with families of record transformations and classify each family as preserving, breaking, neutral, or inapplicable for a basis. Using invariant-defined identity bases and explicit effect models, we derive and certify six classification cells in Lean 4 for scope decomposition, rule refinement, and forking. The derivations show how classifications depend on field granularity, admissible transformation steps, and explicit continuity warrants. We also characterize the identity relations generated by invariant-preserving steps. Two bases generate equal relations exactly when they agree on the preservation of every admissible step in a shared comparison domain, and a single separating step witnesses a difference. The formalization makes identity claims auditable, provides testable conditions for systems that transform records, and exposes the assumptions behind each classification. The results are conditional on the declared bases, models, and warrants, whose adequacy for particular referents requires independent justification.

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