Identifiability of a Shared Continuous Condition from Incompatible Ordinal Standards

Incompatible ordinal standards can describe one underlying condition with different categories and thresholds, so pooling category IDs assumes false equivalence and a shared neural score can appear stable without being identified. We place a structural reportability criterion before amortized prediction. LATENTGRADE defines when co-graded anchors connect the standards, span informative thresholds, and yield well-conditioned local information under a shared scalar-construct assumption; a gauge-fixed latent scale is reportable only for components that pass these diagnostics in a verified measurement design. In controlled recovery, LATENTGRADE reaches latent Spearman correlation 0.92 and threshold RMSE 0.23, compared with 0.84 and 0.47 for shared-latent IRT. On OAI grading, it reaches QWK 0.76 and cross-standard ECE 0.061 versus 0.71 and 0.096; these real-data endpoints measure prediction and agreement, not identification of a universal clinical scale. The controlled anchor and threshold interventions separate predictive fit from identified alignment and show why neural estimation cannot create a common scale absent from the measurement design.