A General Framework for Recovery of Hidden States from Distorted Observations

We propose a unified framework for recovering hidden states from multiple distorted observations generated by a shared underlying event. Observations arise via structured channel transformations combined with additive noise. Recovery quality is governed by transformation invertibility, channel redundancy and independence, and inverse-problem conditioning. Using Fisher information, identifiability theory, and Jacobian conditioning analysis, we delineate three regimes of recoverability: well-posed, ill-conditioned, and unrecoverable. The framework provides a general characterisation of when latent state reconstruction is possible, unstable, or fundamentally ambiguous. The key insight is that recoverability is not determined solely by data availability, but by the geometric and informational structure of the observation process. This provides a principled basis for analysing, designing, and improving multi-channel inference systems. This paper establishes foundational conditions for latent state recoverability in multi-channel observation systems. It forms part of a broader theoretical programme integrating Fisher-information geometry, inverse-problem analysis, and structured inference frameworks.