Fault-Secure Target Identifiability Under Sparse Diagnostic Corruption

This paper develops exact target-specific identifiability criteria for linear diagnostic systems subject to sparse arbitrary corruption. The unknown parameter may remain only partially observable: the objective is not full-state reconstruction, but recovery of a prescribed protected target. Pairwise sparse-fault confusability is therefore treated as a quotient problem, yielding an exact kernel and rank criterion for whether the target remains well defined under every admitted fault support. For a finite hostile support family, the paper proves a sharp hardware law: the minimum number of unrestricted clean scalar augmentations equals the largest target-changing residual rank exposed by any one admissible support. If the new clean bank must also survive f complete erasures, the minimum increases by exactly f. A single coded augmentation can therefore protect an entire finite support library without reconstructing the full mechanism. Structural identifiability and finite-noise robustness nevertheless separate sharply. For K equally spaced hostile residual lines in ℝ², one scalar measurement remains structurally sufficient for every finite K, while the optimal worst-support gain is sin(π/(2K)) and the corresponding Gaussian repetition burden grows as Θ(K²). For dense hostile families, every sub-full-dimensional readout has zero uniform singular margin; for the complete Grassmannian, full target-dimensional readout becomes structurally necessary. A quotient-first generalized singular margin then profiles nuisance, calibration and fault directions before target normalization. The results are finite-dimensional linear geometry. Quantum Hamiltonian identification is one application, but no automatic physical realizability of the mathematically optimal measurements is assumed.