What Is Reusable Across LoRA Runs? The Base-Conditioned Core as a Relational Unit

PEFT makes task adaptation modular: a small LoRA update can be trained once, stored in an adapter library, and transferred or composed without retraining the full model. This workflow raises a practical question: when independently trained updates move to a new run, what preserves their function? We answer that reuse is carried by a base-conditioned core–base relation jointly determined by the donor–target frame relation, the learned core, and the target base. We introduce Bilateral Target-Frame Functional Registration (BTF-FR), which expresses a donor core in the target frame and evaluates the resulting dense intervention in the target model. Functional controls show that registered interventions recover same-task behavior, while raw splicing and spectrum- or norm-matched controls reveal the specific contribution of registration; related task and interface conditions produce an ordered response. BTF-FR therefore provides a functional and auditable criterion for organizing cross-run adapter reuse around donor–target relations and target bases.