A Model Zoo Is Not a List: Clone- and Reparameterization-Invariant Predictive Aggregation

A model zoo is usually treated as a list whose rows receive prior mass. Saving a checkpoint twice, sampling a regularization path more densely, or renaming its coordinate changes the aggregate, although the encoded predictive family is unchanged. We remove this registry representation bias with representation-invariant measure ensembling (RIME), an output-only few-shot adapter that replaces row counts with quotient mass over exact predictive atoms and Hellinger arc mass along declared scalar paths. Under the declared family, path-order, embedding, and target-slice conventions, RIME is provably invariant to exact clone splitting and smooth monotone reparameterization; finite grid refinement is only approximately stable, with a bounded residual. We evaluate a 41-row registry on four benchmarks, two of them under pre-specified protocols. Duplicating one PACS branch sixteen times moves flat-row aggregation by up to 0.583 total variation, whereas RIME is invariant up to floating-point precision and cuts near-clone drift 440-fold. A NICO++ confirmation, planned before its download, reproduces both effects. Invariance is not paid for in accuracy: RIME has the lowest mean Brier of fifteen output-only methods. Against a matched family-balanced control it ties at 4 labels/class and gains 0.00069 at 16, 0.7% of the adaptation gain and unconfirmed under target-level clustering. The evidence supports representation stability at no measured predictive cost, not general baseline superiority: a zoo's bookkeeping can stop being a modeling decision. Code is available at https://anonymous.4open.science/r/rime-B03C.