VARET: Decomposing Robustness for Multi-Site Phonocardiogram Classification under Missing Auscultation Sites and Cohort Shift

Multi-site phonocardiogram (PCG) models are routinely called ``robust'', but the term conflates two failure modes: valves that were never recorded, and cohorts that differ from the training population. We introduce VARET (Valve-Aware Robust Embedding Transformer) to measure these axes separately. VARET encodes each auscultation site with a frozen, CirCor-held-out CardioPHON encoder, collapses a variable number of recordings per valve into one site token, and fuses only the observed sites through a mask-aware pooling path plus a Transformer residual whose scale is initialized at zero, trained under stochastic site dropout. On CirCor DigiScope, VARET readouts reach patient-level AUROC 0.669 against 0.599 (CNN14) and 0.608 (AST) trained from scratch under an identical split and data budget. As valves are progressively removed, the zero-initialized residual degrades least (mean $\Delta$AUROC $+0.010$, versus $+0.019$ for pooling and $+0.032$ for gated fusion), confirming robustness on the first axis. On the second axis the result is negative and, we argue, more informative: zero-shot transfer to BMD-HS and Heart Sound Regurgitation is at or below chance for VARET and for CNN14, yet a linear probe on the same frozen embeddings reaches BMD-HS AUROC $\approx$0.85 with 20\% of target labels and $\approx$0.90 with 50\%. The representation therefore carries transferable information that the CirCor-fitted decision boundary cannot express. Site-level probes show valve informativeness is asymmetric and cohort-dependent (PV 0.646, TV 0.634, MV 0.577, AV 0.559 on a pediatric cohort), and that gains from removing a valve reflect pooling dilution, not clinical redundancy. Missing-site robustness and cohort robustness must be claimed, and measured, independently.