What pathology foundation models can and cannot recover from H&E in rare cancers: a pre-registered molecular-biomarker benchmark across seven TCGA cohorts

Version 3 (29 May 2026). v1 28 May 2026; v2 29 May 2026. Version 3 corrects the morphological-plausibility interpretation — the pre-registered per-cell plausibility ranking did not predict recoverability, now reported as a methodological caution — positions the released evaluation harness as the methodological contribution, and moves the attention figure to the supplement. The analysis, data, and all numerical results are unchanged from version 1. Background and Objective: Pathology foundation models (FMs) predict molecular biomarkers from H&E with strong performance in common cancers, but benchmarks overwhelmingly target high-volume TCGA cohorts and exclude rare cancers — exactly where molecular profiling is least often ordered. We map which molecular biomarkers frozen FM embeddings can and cannot recover from H&E across seven rare TCGA cohorts. Methods: Per a frozen pre-registration, we benchmarked frozen UNI2-h slide embeddings (Prov-GigaPath as a comparison) across ACC, UVM, MESO, CHOL, THYM, KICH and DLBC (524 patients), evaluating 28 powered binary cohort × biomarker cells with patient-level stratified 5-fold cross-validation, an L2-regularised logistic-regression linear probe (primary) and gated-attention multiple-instance learning (secondary). We report pooled out-of-fold AUROC with 1000× bootstrap confidence intervals, permutation tests with Benjamini–Hochberg FDR correction, and pre/post-Platt expected calibration error. A CPTAC COAD MSI baseline-replication gate was passed first. Results: Five cells were recoverable under FDR: DLBC MSI-H (AUROC 0.939; a MANTIS-score-defined instability label, not the clinical entity), THYM GTF2I (0.933; partly confounded by WHO subtype), THYM TMB-high (0.828), UVM EIF1AX (0.817) and UVM chromosome-3 loss (0.794); four hold under the conservative Benjamini–Yekutieli correction. Mean AUROC was 0.643. Outside the positives the map is a single indeterminate zone — at n=48–124 a near-chance AUROC is the absence of evidence, not evidence of absence. The attention model and a second FM did not beat the linear probe, and zero-shot transfer from common cohorts largely failed. Conclusions: Frozen FM embeddings yield a calibrated, FDR-controlled recoverability map for rare-cancer molecular biomarkers — recovering a few morphologically grounded signals while leaving most indeterminate — rather than a deployable clinical triage tool.