Gaussian relative entropy is oriented as smoother relative to filter. A
normal aci() call uses the supplied-code backward-ODE headline smoother,
including its correlated-noise correction, independently of keep.
lag_table() and aci(table = ...) instead use the complete online
Theorem 3 smoother; their finite-grid diagonal can therefore differ from
headline ACI. aci_range() summarizes the duration of influence on the
discrete time grid. A finite adaptive table is labelled
objective_on_truncated_table; its tail_bound field is a heuristic tail
estimate and must not be interpreted as a certified error bound. The
l1_linf estimator is a ratio: the forward ratio and the exact form are
integrated with composite Simpson, following the ACI reference code.
References
Andreou, M. and Chen, N. (2026). Bridging prediction and attribution: identifying forward and backward causal influence ranges using assimilative causal inference. arXiv:2510.21889v2, 4 August 2026. doi:10.48550/arXiv.2510.21889