This technical note presents a minimal reproducible diagnostic test of calibration under non-invertible measurement mappings. Using a controlled synthetic setup, the note shows that local calibration can produce low error within a restricted regime while failing to preserve comparability outside it. A reference measurement channel with approximately linear response is paired with a second channel exhibiting global non-invertibility (saturation/compression). Models trained within a calibration window remain locally accurate but display systematic error growth and loss of distinction outside that domain. The result is consistent across multiple model classes (linear, polynomial, and ensemble methods), indicating that increased model capacity does not recover information lost through non-invertible transformations. A minimal empirical framing is provided through independent domains (clinical chemistry commutability, infrared thermography, and air quality sensing), where calibration agreement does not ensure cross-method or cross-context comparability. The supported claim is strictly diagnostic and local: calibration agreement does not, in general, establish transferable comparability when measurement mappings are structurally non-invertible. This record is accompanied by a minimal reproducibility bundle containing the synthetic experiment, output data, and summary statistics supporting the observed behavior. The note does not propose a general theory of measurement and does not challenge standard calibration practices. It isolates a recurring structural condition that may arise across heterogeneous measurement contexts.
Danilo Tavella (Tue,) studied this question.
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