Adaptive Environmental Inference in Multi-Witness Systems

This paper extends the Trace Forensics framework to jointly infer both latent system states and environmental parameters from multiple heterogeneous observation channels (“witnesses”). While earlier work assumes either known environmental transformations or separately inferred parameters, this work introduces a unified model in which the environment itself is treated as an unknown parameterized system. The framework formalizes multi-witness observations as conditionally independent transformations of a shared latent state, governed by environment-dependent operators. The resulting formulation enables simultaneous estimation of the latent state S(t) and environmental parameters θ, along with uncertainty characterization under noise and transformation degeneracy. This work bridges inverse problems, multi-sensor fusion, and adaptive system identification, and serves as a structural extension toward dynamic and temporally evolving inference in subsequent papers.