Conditional Identifiability and Inference for OFT-Derived VGM Measurement Predictions: Nuisance Geometry, Calibration, and an Exact Gaussian Benchmark

Abstract

This paper develops a conditional inverse-analysis layer for OFT/VGM measurement predictions, following the forward-response framework of VGM XIV. It distinguishes equality of observation laws from equality of mean readouts, joint-parameter equivalence from nuisance-family overlap, and structural identification from finite-noise resolution. Efficient score projection and the Fisher Schur complement quantify information retained after nuisance adjustment under stated regularity assumptions. An exact Gaussian continuation of the two-channel measurement benchmark derives the identifiable amplitude, its profile likelihood and sampling variance, the loss of common-mode identification, and the recovery supplied by an independent calibration observation. A proper Gaussian prior yields an explicit posterior that remains equal to the prior when the response vanishes. An exact one-sided boundary-null calculation illustrates why ordinary chi-square calibration cannot be applied indiscriminately. Frequentist and Bayesian constructions are kept distinct, with conditional nuisance laws, uncertainty dependence, and reproducible pre-test choices made explicit. All formulas describe a declared idealized model; no empirical dataset, fitted parameter, detection significance, or microscopic OFT realization is supplied. The release includes symbolic verification and defines the additional products required before a genuinely withheld empirical test.