Allow a representation \(\gamma_t\) to change with time. Define the typed defect
If \(\widehat f_t\) is \(\lambda_t\)-Lipschitz on the relevant domain and \(\|r_t(x_t)\|\leq\delta_t\), the prediction error satisfies
Read the diagram in words
Compare how the same local defect is propagated under different amplification factors. Earlier defects receive products of subsequent factors. These curves are analytical envelopes with declared constants, rather than measured prediction errors.
For a fixed representation \(R\), a reference reduced operator \(B\) and fitted operator \(\widehat B\),
The first term is representational nonclosure. The second is estimation error. They can enter the same propagation inequality after being bounded in the state norm.
The mathematical point
The suffix products determine whether earlier defects are damped or amplified. The chart shows analytical envelopes, not measured prediction errors.
Scope
Both the true represented state and predicted state must remain in the Lipschitz domain. Stability of each action's eigenvalues alone does not certify stability under switching.