What Survives Learned Symbolic Compression?

Lossy text compression for language-model pipelines is judged by reconstruction distance or by downstream task accuracy, and neither says whether the compressed representation still states what the source stated. We measure agreement with a constructed reference for grammar-constrained symbolic codes. The reference represents source facts as equations, and a fixed decoder recovers the equations a code encodes. An exact rule system compares their consequences independently of the code's well-formedness checker. On controlled arithmetic micro-worlds, we evaluate learned translators from 70M to 2.8B parameters against structured controls and learned baselines at matched byte and token budgets. Passing the checker is not preserving the source: a self-consistent mistranslation passes it, and so do sampled learned-translation errors. Across byte budgets, the best learned trace translator trails the strongest compact structured control, with area under the closure-agreement curve of 0.67 against 0.86. Increasing translator size does not close this aggregate gap; the largest Pythia translator matches the best smaller translator's saved byte-axis agreement scores. Source fidelity relative to the constructed reference, internal validity, and what a consumer model recovers are three different quantities and should be measured separately.