Auditing Symbolic-Law Sharing: A Failure-Aware Benchmark for Multi-Environment Scientific Regression

Abstract

Preprint (v0.6). Not peer-reviewed.Scientific law discovery often pools related experiments to identify shared symbolic structure and then adapts a few environment-specific parameters. Pooling can compensate for limited observations, but a poor sharing decision may fit low-range support and still fail in an unseen environment’s tail. We introduce a failure-aware, target-access-controlled benchmark for auditing symbolic transfer across held-out scientific environments. Its inventory covers five real scientific assets; a retrospective global-versus-restricted ledger covers four through 18 dependent contrasts while retaining invalid-domain predictions, failed repetitions, finite catastrophes, protocol timing, and redistribution boundaries. The evidence is deliberately mixed: global sharing and restrictions based on archives, cohorts, geometry, or machining conditions each help in some settings and harm in others. We also audit one frozen source only validation policy over 196 dependent environment-family units from the same four ledger assets. It improves equal-dataset cap-2 mean action regret relative to always-global, but selects seven failed arms versus three, and only 6 of 14 dataset-family cells have a positive score-benefit rank direction. These results expose a conflict between average transfer utility and failure safety. They motivate a minimum reporting contract that separates source-side arm selection, held-out support fitting, and tail evaluation, and reports utility, failures, coverage, and protocol validity separately. The contribution is an evaluation and audit framework, not calibrated abstention or a universally superior symbolic-regression family.