Operational Tomography of Fixed-Ambient Coupled Dynamics: Multi-Detector Completeness, Noise-Whitened Identifiability, and Calibration Gates

This paper develops the local operational layer connecting admitted fixed-ambient coupled dynamics to detector design and parameter inference within the OFT/VGM research programme. Building on Papers XXII–XXIV, it distinguishes structural response rank, noise-weighted precision, and empirical calibration. A finite family of dimensionless readouts defines a forward map and its parameter sensitivity matrix. Full regular first-order identification of p selected parameter directions requires at least p scalar readouts. When the restricted scalar response profiles are linearly independent, their Gram duals provide p signed detector windows with identity sensitivity at a declared nominal point. These windows are held fixed during parameter differentiation; the construction does not establish unrestricted positive-window or hardware feasibility. For a declared positive-definite noise covariance, the covariance-weighted information matrix is invariant under invertible detector recombinations. A local linearized least-squares error bound is controlled by the smallest parameter-direction singular value, including null directions when detector count is insufficient. The Cramér–Rao interpretation is restricted to the stated Gaussian likelihood and regular locally unbiased estimators. Independent detector augmentation is information-monotone. A conditional-noise formula extends this covariance-weighted monotonicity to correlated added channels, while a least-eigenspace criterion identifies when a single added row strictly improves the weakest direction. An illustrative clock-plus-scalar protocol separates an unknown clock normalization from physical field parameters. Residual degrees of freedom and a calibration ledger distinguish parameter identification from a data-bearing lack-of-fit test. The results are local, theoretical, and conditional on the declared solution family, parameter scaling, detector definitions, and noise model. No empirical parameter fit is performed. Operational tomography here means recovery of selected parameter directions from multiple readouts; the manuscript does not implement X-ray computed tomography or establish a radiation-dose reduction. This deposit contains the English manuscript, revised version 1.1 dated 8 November 2026, its XeLaTeX source, and the accompanying Peaceful Civilian Use Licence. Version 1.1 updates the published references, clarifies regularity and fixed-window assumptions, includes null parameter directions in the singular-value convention, and adds correlated-noise augmentation and clock-scale distinctions. Series: OFT/VGM Research Programme — Paper XXV.DOI: https://doi.org/10.5281/zenodo.24059931