Conditional Measurement Response for OFT-Derived VGM Observable Fingerprints: Transfer, Calibration, Uncertainty, and an Exact Two-Channel Benchmark

This paper formulates the forward measurement layer connecting a declared OFT/VGM theoretical observable to an instrument readout. It separates mathematical contrast, detector visibility, nuisance-robust separation, and statistical detection. Linear and nonlinear responses are treated with explicit validity domains, sampling conventions, calibration coupling, and joint uncertainty propagation. A weighted projection identifies local response directions that survive calibration and acquisition nuisance, while a Lipschitz bound supplies a sufficient finite-contrast separation criterion. An exact idealized two-channel benchmark exhibits response-rank loss, a calibration-degenerate signal, and a common-mode-free contrast whose bounded-error separation condition is derived analytically. Shared calibration and cross-covariances are retained in contrast uncertainty; geometric error sets are distinguished from probability laws. The benchmark is a reproducible mathematical example, not a characterized detector, a realized VGM-XIII source solution, or experimental evidence. The resulting prediction contract states what must be fixed before subsequent identifiability analysis and withheld testing. No empirical dataset, detection significance, or microscopic OFT realization is claimed.