Scientific foundation models are commonly evaluated after heterogeneous physical problems have already been translated into a compatible gridded, tokenized or symbolic representation. This leaves the scientific interface outside both the pretrained model and the audit of what is actually reused. We study the complementary setting in which boundary histories, sparse monitor records and loading histories retain their native inference classes and their outputs remain on Cartesian, latitude-longitude and unstructured domains. GEODE couples task-specific scientific interfaces to a shared routed library of wavelet operators. A single jointly pretrained model represents cavity flow, radiation dose and elastoplastic stress, then acquires a heat exchanger and a reactor subchannel by training a private interface containing 2.1% of its parameters. Earlier predictions remain unchanged by parameter isolation, whereas unrestricted fine-tuning degrades them by factors of 14-29. Crucially, preservation alone does not establish reuse: norm-matched randomized-library controls show that the contribution of pretrained computation is conditional on the task and data regime. A separate decomposition shows that full-field relative L2 error can substantially understate error relative to spatial variation when field level dominates the norm. Task-specific operators remain more accurate on three of the five problems. These results distinguish multi-task coverage, preservation and pretrained reuse as separate properties that must be tested independently when scientific foundation models span heterogeneous interfaces.

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