Physical Response Is Boundary-Invariant, Internal Attribution Is Not.

Reduced descriptions of hidden Markov environments require choices about how unresolved or irreversible transitions are completed. This article separates two questions that are often conflated: whether a measured linear response is fixed by the physical boundary description, and whether its internal mechanistic attribution is fixed as well. For finite irreducible Markov dynamics, we classify source visibility through a projected Poisson response and distinguish it from an independent propagator axis. We then define boundary-equivalent families of hidden-state completions and prove that the response and its control derivative converge to common boundary values. The internal source–propagator attribution at finite completion is nevertheless non-identifiable. A constructive family of 24 admissible lifts and 576 exact decompositions spans more than an order of magnitude in the source-to-propagator norm ratio and includes both relative orientations, although all members share the same physical boundary operators. Along the canonical completion, the qualitative diagnosis reverses from source-dominated and counter-oriented to propagator-dominated and co-oriented at the boundary. The theory is supported by an exactly solvable hidden-environment benchmark and an independent continuous campaign of 128 backgrounds comprising more than four hundred million stochastic events. Complete proofs, numerical contracts, and robustness analyses are included in the article; the complete decomposition register is supplied as machine-readable supplementary data. The results delimit which response statements can be transferred across hidden completions and which mechanistic explanations must remain model-qualified.