Interpretability Bounds for Contrastive Medical Image Embeddings Under Scanner Vendor Proprietary Post-Processing Pipelines: A Computer Fairness Estimation

Contrastive medical image embeddings are increasingly used for downstream clinical tasks, yet their interpretability is bounded by scanner vendor proprietary post-processing pipelines that alter image statistics in ways invisible to the embedding model. the present analysis formalises that bound and estimates its consequences for computer fairness. We define a vendor-induced representation shift as a measurable divergence between embedding distributions across scanner manufacturers, and we derive an interpretability bound that links the shift to the maximum attainable fairness of any downstream classifier. The bound is evaluated through a replication-based design study using a before-after-control-impact estimator with a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64). Power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required to detect a 5-percentage-point fairness effect at 80% power. The results show that interpretability bounds tighten sharply as cluster count falls below 24, and that the minimum detectable effect at 80% power exceeds 8 percentage points for 8 clusters. Fairness estimation for contrastive medical embeddings must treat vendor post-processing as a structural confounder rather than a nuisance parameter, and it specifies the design conditions under which interpretability claims remain defensible.