Statistical data editing in official statistics must restore consistency while limiting changes to observed data. Exact minimum-change correction can be computationally demanding. This paper develops a general framework for structured data whose dependencies admit a normalized acyclic routing representation. It connects routing metadata and explicitly specified semantic edits to logical admissibility, violation diagnosis, and correction. Under stated record semantics, the generated Horn theory characterizes admissibility without materializing its deductive closure. Canonical indices preserve the origin of each requirement and identify the variables that can affect a violation. With complete diagnostics and strictly positive weights, a nonnegative violation Hamiltonian vanishes exactly on admissible records within the specified domain. This characterization is independent of the correction procedure and provides both an objective for correction and a certificate: a verified zero-energy output is admissible and globally minimizes violation energy within its permitted candidate domain. Minimum modification cost is formulated separately, with sufficient conditions for an equivalent penalized objective and optimality certificates based on attained lower bounds. A household survey application illustrates the construction, the verification of admissible corrections, and minimum-cost certification for a subset of outputs. The framework supports traceable validation and correction in official statistics, while statistical accuracy of replacement values requires separate assessment.

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