Learning Hidden Constants Through Certified Renaming

Known-constant learners for equality register automata require the distinguished data values to be supplied. We study deterministic membership-query learning when only an upper bound on the size of the target language's global support is known. A wrapper replaces selected atoms by pairwise disjoint sets of probe values. Bounded contamination gives an exact generic membership answer without identifying a genuinely fresh probe. A disagreement with the original answer isolates one essential constant by bisection. We prove that the resulting oracle is invariant under permutations fixing the discovered constants, establish closure for deterministic equality register languages, and give a conditional reduction to any complete learner for the purified class. With an exact equivalence oracle, the reduction terminates after at most one restart per essential constant and returns the least support. An implementation wraps unmodified RALib and is evaluated on existing protocol models, authored predicates in three execution engines, and two configured Java queues. Query costs improve on some controls and worsen on others. The contribution is certified support discovery and consistent oracle simulation; practical equivalence testing and universal efficiency are not established. Substantial OpenAI Codex assistance in method exploration, proof drafting, code, experiments and writing is disclosed in the manuscript. This is a preprint, not peer-reviewed research. The accompanying package includes source, full experimental records, proof arguments and an integrity manifest. Exact results require the stated deterministic equality semantics, support-size bound and equivalence oracle. No production EMILIA integration is claimed. License scope: the paper, documentation and experimental records are CC BY 4.0; original source code is MIT. See LICENSES.txt and LICENSE-MIT.txt inside the accompanying archive. Third-party dependencies retain their own licenses.